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What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

  • The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
  • The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
  • The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
  • The calculus section will carry out differentiation as well as definite and indefinite integration.
  • The matrices section contains commands for the arithmetic manipulation of matrices.
  • The graphs section contains commands for plotting equations and inequalities.
  • The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

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Algebra Solver to Check Your Homework

Algebra Calculator with Steps free | Algebra Solver

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The algebra calculator that we present here is a great tool to solve a large number of algebraic problems. This algebra calculator allows you to find the step-by-step solution of: first, second and third degree equations, absolute value equations and systems of equations, mathematical inequalities. With our algebraic calculator you will also be able to simplify and factor polynomials, solve equations with more than one variable, solve trigonometric equations, perform all kinds of operations with polynomials and evaluate mathematical expressions.

This algebraic calculator will be your ideal companion to study and understand algebra perfectly.

In order for you to get the most out of this calculator, we recommend that you read the instructions just below.

Table of Contents

  • 1 Algebra Calculator
  • 2.1 Input user interface
  • 2.2 Output interface
  • 3 Supported operations
  • 4 The Benefits of Using an Online Algebra Calculator in the Classroom

Instructions for using the Online Algebra Calculator

The algebra calculator has a very intuitive and friendly interface which makes it very easy to use. To explain in a simple way how to use it, we will first explain the elements of the input interface, through which you can enter the mathematical expressions you want to solve. Then we will explain the output interface, through which the calculator displays the solution.

Algebra Calculator User Interface - Part A

Input user interface

The input user interface is subdivided into 4 parts according to their functionality, which are shown in figure 1.

  • Input field: This is where you write the algrebraic expression you want to solve. You can do this using the keyboard of your device or the virtual keyboard of the calculator itself. You should use only the functions and operators that are presented in Table 1.
  • Input to mathematical notation: In this box, the expression entered in the input field is rewritten using mathematical notation.
  • Choose between degrees or radians
  • Enable or disable trigonometric functions on the virtual keyboard
  • Choose the variable for which you want to solve the entered equation.
  • Virtual keyboard: In it are all the functions, constants and functions that you can use in the algebra calculator. Pressing the “Trig Frunctions” button on the tool bar displays the buttons for all trigonometric and hyperbolic functions.

Output interface

The solution to the entered mathematical expression is displayed in the output interface. Depending on the nature of the mathematical problem, options may be generated to explore other variants of the solution. For example, if you’ve entered a quadratic equation, you’ll be able to choose a different solving method, or if you’ve entered an equation with more than one variable, you’ll be able to select which other variable you want to solve the equation for.

algebra 2 problem solver with steps

Table 1: Valid functions and symbols

Supported operations

The online Algebra Calculator is a useful tool for performing a wide range of mathematical operations. With this calculator, users can solve linear equations, find the roots of quadratic equations, and even solve third and fourth degree equations. It can also be used to factor and simplify algebraic expressions and polynomials, as well as perform operations with polynomials including addition, subtraction, multiplication, and division.

In addition to these features, the Algebra Calculator can also be used to solve systems of equations, perform operations with complex numbers, and work with fractions. It is also capable of solving inequalities, evaluating equations, and calculating equations with fractions and radicals.

The calculator can even handle more advanced operations such as solving logarithmic and exponential equations, as well as trigonometric equations. It can also be used to solve for x and y, and to solve inequalities and equations with absolute value. And for those working on permutation exercises, the calculator can provide assistance there as well.

Overall, the online Algebra Calculator is a versatile tool that can save time and effort when solving a wide range of algebraic problems. Whether you are a student, a teacher, or simply someone looking to brush up on your algebra skills, this calculator can be an invaluable resource.

Here is the list of mathematical operations that you can perform with the online algrebra calculator:

  • Solve linear equations
  • Finding the roots of quadratic equations
  • Solve third degree and fourth degree equations
  • Factor and simplify algebraic expressions and/or polynomials
  • Perform operations with polynomials (addition, subtraction, multiplication and division of polynomials)
  • Solve systems of equations equations
  • Perform operations with complex numbers
  • Perform operations with fractions
  • Solve inequalities
  • Evaluate equations
  • Calculate equations with fractions
  • Calculate equations with radicals
  • Solve lagarithmic equations
  • Solve exponential equations
  • Solve trigonometric equations
  • Solve for x
  • Solve for yyy
  • Solve inequalities and equations with absolute value
  • Solve permutation exercises
  • Among other…

The Benefits of Using an Online Algebra Calculator in the Classroom

The online Algebra Calculator is a valuable tool for students and teachers in the classroom. This calculator allows users to perform a wide range of algebraic operations and solve equations quickly and accurately, saving time and effort in the process.

One of the main benefits of using the online Algebra Calculator in school is that it can help students to better understand algebraic concepts. By using the calculator to solve equations and perform operations, students can see firsthand how algebra works and how it can be used to solve real-world problems. This can be particularly helpful for students who are struggling to grasp the concepts being taught in class.

The online Algebra Calculator can also be a useful resource for teachers. It can be used to demonstrate algebraic concepts to students, as well as to check the accuracy of students’ work. In addition, teachers can use the calculator to create online quizzes and assignments, allowing students to practice their algebra skills in a convenient, interactive way.

Overall, the use of the online Algebra Calculator in the classroom can be a valuable aid for both students and teachers. By providing a convenient, accurate way to perform algebraic operations and solve equations, the calculator can help to make learning algebra more enjoyable and effective.

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How to Solve Algebra Problems Step-By-Step

  • Pre Algebra & Algebra
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  • B.B.A., Finance and Economics, University of Oklahoma

Solving Algebra word problems is useful in helping you to solve earthly problems. While the 5 steps of Algebra problem solving are listed below, the following will help you learn how to first identify the problem.

  • Identify the problem.
  • Identify what you know.
  • Make a plan.
  • Carry out the plan.
  • Verify that the answer makes sense.

Identify the Problem

Back away from the calculator ; use your brain first. Your mind analyzes, plans, and guides in the labyrinthine quest for the solution. Think of the calculator as merely a tool that makes the journey easier. After all, you wouldn’t want a surgeon to crack your ribs and perform a heart transplant without first identifying the source of your chest pains.

The steps of identifying the problem are:

  • Express the problem question or statement.
  • Identify the unit of the final answer.

Express the Problem Question or Statement

In Algebra word problems, the problem is expressed as either a question or a statement.

  • How many trees will John have to plant?
  • How many televisions will Sara have to sell to earn $50,000?
  • Find the number of trees John will have to plant.
  • Solve for the number of televisions Sara will have to sell to earn $50,000.

Identify the Unit of the Final Answer

What will the answer look like? Now that you understand the word problem’s purpose, determine the answer’s unit. For example, will the answer be in miles, feet, ounces, pesos, dollars, the number of trees, or a number of televisions?

Algebra Word Problem

Javier is making brownies to serve at the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if 60 people attend the picnic?
  • Identify the problem:   How many cups will Javier need if 60 people attend the picnic?
  • Identify the unit of the final answer: Cups
In the market for computer batteries, the intersection of the supply and demand functions determines the price, p dollars , and the quantity, q , of goods sold. Supply function: 80 q - p = 0 Demand function: 4 q + p = 300 Determine the price and quantity of computer batteries sold when these functions intersect.
  • Identify the problem:   How much will the batteries cost and how much will be sold when supply and demand functions meet?
  • Identify the unit of the final answer: The quantity, or q , will be given in batteries. The price, or p , will be given in dollars.
  • Proportions Word Problems Worksheet 1
  • Proportions Word Problems Worksheet: Answers and Explanations
  • How to Do Algebra Word Problems
  • How to Solve Proportions to Adjust a Recipe
  • Algebra Age-Related Word Problem Worksheets
  • Lesson Plan: Addition and Subtraction with Pictures
  • The Quantity Theory of Money
  • Stoichiometry Definition in Chemistry
  • 2nd Grade Math Word Problems
  • Math Glossary: Mathematics Terms and Definitions
  • Ideas for Thanksgiving Math Word Problems
  • Sixth Grade Word Problems
  • Quiz 8th-Graders With These Math Word Problems
  • Learn to Calculate Percent Change
  • How to Cancel Units - Chemistry Metric Conversions
  • Simple Interest Worksheets With Answers

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Course: 7th grade   >   Unit 6

  • Same thing to both sides of equations
  • Intro to two-step equations
  • Two-step equations intuition
  • Worked example: two-step equations

Two-step equations

  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

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Solving equations

Here you will learn about solving equations, including linear and quadratic algebraic equations, and how to solve them.

Students will first learn about solving equations in grade 8 as a part of expressions and equations, and again in high school as a part of reasoning with equations and inequalities.

What is solving an equation?

Solving equations is a step-by-step process to find the value of the variable. A variable is the unknown part of an equation, either on the left or right side of the equals sign. Sometimes, you need to solve multi-step equations which contain algebraic expressions.

To do this, you must use the order of operations, which is a systematic approach to equation solving. When you use the order of operations, you first solve any part of an equation located within parentheses. An equation is a mathematical expression that contains an equals sign.

For example,

\begin{aligned}y+6&=11\\\\ 3(x-3)&=12\\\\ \cfrac{2x+2}{4}&=\cfrac{x-3}{3}\\\\ 2x^{2}+3&x-2=0\end{aligned}

There are two sides to an equation, with the left side being equal to the right side. Equations will often involve algebra and contain unknowns, or variables, which you often represent with letters such as x or y.

You can solve simple equations and more complicated equations to work out the value of these unknowns. They could involve fractions, decimals or integers.

What is solving an equation?

Common Core State Standards

How does this relate to 8 th grade and high school math?

  • Grade 8 – Expressions and Equations (8.EE.C.7) Solve linear equations in one variable.
  • High school – Reasoning with Equations and Inequalities (HSA.REI.B.3) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

[FREE] Math Equations Check for Understanding Quiz (Grade 6 to 8)

[FREE] Math Equations Check for Understanding Quiz (Grade 6 to 8)

Use this quiz to check your grade 6 to 8 students’ understanding of math equations. 10+ questions with answers covering a range of 6th, 7th and 8th grade math equations topics to identify areas of strength and support!

How to solve equations

In order to solve equations, you need to work out the value of the unknown variable by adding, subtracting, multiplying or dividing both sides of the equation by the same value.

  • Combine like terms .
  • Simplify the equation by using the opposite operation to both sides.
  • Isolate the variable on one side of the equation.

Solving equations examples

Example 1: solve equations involving like terms.

Solve for x.

Combine like terms.

Combine the q terms on the left side of the equation. To do this, subtract 4q from both sides.

The goal is to simplify the equation by combining like terms. Subtracting 4q from both sides helps achieve this.

After you combine like terms, you are left with q=9-4q.

2 Simplify the equation by using the opposite operation on both sides.

Add 4q to both sides to isolate q to one side of the equation.

The objective is to have all the q terms on one side. Adding 4q to both sides accomplishes this.

After you move the variable to one side of the equation, you are left with 5q=9.

3 Isolate the variable on one side of the equation.

Divide both sides of the equation by 5 to solve for q.

Dividing by 5 allows you to isolate q to one side of the equation in order to find the solution. After dividing both sides of the equation by 5, you are left with q=1 \cfrac{4}{5} \, .

Example 2: solve equations with variables on both sides

Combine the v terms on the same side of the equation. To do this, add 8v to both sides.

7v+8v=8-8v+8v

After combining like terms, you are left with the equation 15v=8.

Simplify the equation by using the opposite operation on both sides and isolate the variable to one side.

Divide both sides of the equation by 15 to solve for v. This step will isolate v to one side of the equation and allow you to solve.

15v \div 15=8 \div 15

The final solution to the equation 7v=8-8v is \cfrac{8}{15} \, .

Example 3: solve equations with the distributive property

Combine like terms by using the distributive property.

The 3 outside the parentheses needs to be multiplied by both terms inside the parentheses. This is called the distributive property.

\begin{aligned}& 3 \times c=3 c \\\\ & 3 \times(-5)=-15 \\\\ &3 c-15-4=2\end{aligned}

Once the 3 is distributed on the left side, rewrite the equation and combine like terms. In this case, the like terms are the constants on the left, –15 and –4. Subtract –4 from –15 to get –19.

Simplify the equation by using the opposite operation on both sides.

The goal is to isolate the variable, c, on one side of the equation. By adding 19 to both sides, you move the constant term to the other side.

\begin{aligned}& 3 c-19+19=2+19 \\\\ & 3 c=21\end{aligned}

Isolate the variable to one side of the equation.

To solve for c, you want to get c by itself.

Dividing both sides by 3 accomplishes this.

On the left side, \cfrac{3c}{3} simplifies to c, and on the right, \cfrac{21}{3} simplifies to 7.

The final solution is c=7.

As an additional step, you can plug 7 back into the original equation to check your work.

Example 4: solve linear equations

Combine like terms by simplifying.

Using steps to solve, you know that the goal is to isolate x to one side of the equation. In order to do this, you must begin by subtracting from both sides of the equation.

\begin{aligned} & 2x+5=15 \\\\ & 2x+5-5=15-5 \\\\ & 2x=10 \end{aligned}

Continue to simplify the equation by using the opposite operation on both sides.

Continuing with steps to solve, you must divide both sides of the equation by 2 to isolate x to one side.

\begin{aligned} & 2x \div 2=10 \div 2 \\\\ & x= 5 \end{aligned}

Isolate the variable to one side of the equation and check your work.

Plugging in 5 for x in the original equation and making sure both sides are equal is an easy way to check your work. If the equation is not equal, you must check your steps.

\begin{aligned}& 2(5)+5=15 \\\\ & 10+5=15 \\\\ & 15=15\end{aligned}

Example 5: solve equations by factoring

Solve the following equation by factoring.

Combine like terms by factoring the equation by grouping.

Multiply the coefficient of the quadratic term by the constant term.

2 x (-20) = -40

Look for two numbers that multiply to give you –40 and add up to the coefficient of 3. In this case, the numbers are 8 and –5 because 8 x -5=–40, and 8+–5=3.

Split the middle term using those two numbers, 8 and –5. Rewrite the middle term using the numbers 8 and –5.

2x^2+8x-5x-20=0

Group the terms in pairs and factor out the common factors.

2x^2+8x-5x-20=2x(x + 4)-5(x+4)=0

Now, you’ve factored the equation and are left with the following simpler equations 2x-5 and x+4.

This step relies on understanding the zero product property, which states that if two numbers multiply to give zero, then at least one of those numbers must equal zero.

Let’s relate this back to the factored equation (2x-5)(x+4)=0

Because of this property, either (2x-5)=0 or (x+4)=0

Isolate the variable for each equation and solve.

When solving these simpler equations, remember that you must apply each step to both sides of the equation to maintain balance.

\begin{aligned}& 2 x-5=0 \\\\ & 2 x-5+5=0+5 \\\\ & 2 x=5 \\\\ & 2 x \div 2=5 \div 2 \\\\ & x=\cfrac{5}{2} \end{aligned}

\begin{aligned}& x+4=0 \\\\ & x+4-4=0-4 \\\\ & x=-4\end{aligned}

The solution to this equation is x=\cfrac{5}{2} and x=-4.

Example 6: solve quadratic equations

Solve the following quadratic equation.

Combine like terms by factoring the quadratic equation when terms are isolated to one side.

To factorize a quadratic expression like this, you need to find two numbers that multiply to give -5 (the constant term) and add to give +2 (the coefficient of the x term).

The two numbers that satisfy this are -1 and +5.

So you can split the middle term 2x into -1x+5x: x^2-1x+5x-5-1x+5x

Now you can take out common factors x(x-1)+5(x-1).

And since you have a common factor of (x-1), you can simplify to (x+5)(x-1).

The numbers -1 and 5 allow you to split the middle term into two terms that give you common factors, allowing you to simplify into the form (x+5)(x-1).

Let’s relate this back to the factored equation (x+5)(x-1)=0.

Because of this property, either (x+5)=0 or (x-1)=0.

Now, you can solve the simple equations resulting from the zero product property.

\begin{aligned}& x+5=0 \\\\ & x+5-5=0-5 \\\\ & x=-5 \\\\\\ & x-1=0 \\\\ & x-1+1=0+1 \\\\ & x=1\end{aligned}

The solutions to this quadratic equation are x=1 and x=-5.

Teaching tips for solving equations

  • Use physical manipulatives like balance scales as a visual aid. Show how you need to keep both sides of the equation balanced, like a scale. Add or subtract the same thing from both sides to keep it balanced when solving. Use this method to practice various types of equations.
  • Emphasize the importance of undoing steps to isolate the variable. If you are solving for x and 3 is added to x, subtracting 3 undoes that step and isolates the variable x.
  • Relate equations to real-world, relevant examples for students. For example, word problems about tickets for sports games, cell phone plans, pizza parties, etc. can make the concepts click better.
  • Allow time for peer teaching and collaborative problem solving. Having students explain concepts to each other, work through examples on whiteboards, etc. reinforces the process and allows peers to ask clarifying questions. This type of scaffolding would be beneficial for all students, especially English-Language Learners. Provide supervision and feedback during the peer interactions.

Easy mistakes to make

  • Forgetting to distribute or combine like terms One common mistake is neglecting to distribute a number across parentheses or combine like terms before isolating the variable. This error can lead to an incorrect simplified form of the equation.
  • Misapplying the distributive property Incorrectly distributing a number across terms inside parentheses can result in errors. Students may forget to multiply each term within the parentheses by the distributing number, leading to an inaccurate equation.
  • Failing to perform the same operation on both sides It’s crucial to perform the same operation on both sides of the equation to maintain balance. Forgetting this can result in an imbalanced equation and incorrect solutions.
  • Making calculation errors Simple arithmetic mistakes, such as addition, subtraction, multiplication, or division errors, can occur during the solution process. Checking calculations is essential to avoid errors that may propagate through the steps.
  • Ignoring fractions or misapplying operations When fractions are involved, students may forget to multiply or divide by the common denominator to eliminate them. Misapplying operations on fractions can lead to incorrect solutions or complications in the final answer.

Related math equations lessons

  • Math equations
  • Rearranging equations
  • How to find the equation of a line
  • Solve equations with fractions
  • Linear equations
  • Writing linear equations
  • Substitution
  • Identity math
  • One step equation

Practice solving equations questions

1. Solve 4x-2=14.

GCSE Quiz False

Add 2 to both sides.

Divide both sides by 4.

2. Solve 3x-8=x+6.

Add 8 to both sides.

Subtract x from both sides.

Divide both sides by 2.

3. Solve 3(x+3)=2(x-2).

Expanding the parentheses.

Subtract 9 from both sides.

Subtract 2x from both sides.

4. Solve \cfrac{2 x+2}{3}=\cfrac{x-3}{2}.

Multiply by 6 (the lowest common denominator) and simplify.

Expand the parentheses.

Subtract 4 from both sides.

Subtract 3x from both sides.

5. Solve \cfrac{3 x^{2}}{2}=24.

Multiply both sides by 2.

Divide both sides by 3.

Square root both sides.

6. Solve by factoring:

Use factoring to find simpler equations.

Set each set of parentheses equal to zero and solve.

x=3 or x=10

Solving equations FAQs

The first step in solving a simple linear equation is to simplify both sides by combining like terms. This involves adding or subtracting terms to isolate the variable on one side of the equation.

Performing the same operation on both sides of the equation maintains the equality. This ensures that any change made to one side is also made to the other, keeping the equation balanced and preserving the solutions.

To handle variables on both sides of the equation, start by combining like terms on each side. Then, move all terms involving the variable to one side by adding or subtracting, and simplify to isolate the variable. Finally, perform any necessary operations to solve for the variable.

To deal with fractions in an equation, aim to eliminate them by multiplying both sides of the equation by the least common denominator. This helps simplify the equation and make it easier to isolate the variable. Afterward, proceed with the regular steps of solving the equation.

The next lessons are

  • Inequalities
  • Types of graph
  • Coordinate plane

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  • Powers of i
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  • Is Polynomial
  • Leading Coefficient
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  • Standard Form
  • Complete the Square
  • Synthetic Division
  • Linear Factors
  • Rationalize Denominator
  • Rationalize Numerator
  • Identify Type
  • Convergence
  • Interval Notation
  • Pi (Product) Notation
  • Boolean Algebra
  • Truth Table
  • Mutual Exclusive
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  • Caretesian Product
  • EN: age-word-problems-calculator menu
  • EN: distance-word-problems-calculator menu
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Number line.

  • \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
  • \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
  • \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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  • High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,... Read More

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