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What do you want to calculate.

## Example (Click to try)

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## Solving Equations

An equation says that two things are equal. It will have an equals sign "=" like this:

what is on the left (x − 2) equals what is on the right (4)

So an equation is like a statement " this equals that "

## What is a Solution?

A Solution is a value we can put in place of a variable (such as x ) that makes the equation true .

## Example: x − 2 = 4

When we put 6 in place of x we get:

How about other values for x ?

- For x=5 we get "5−2=4" which is not true , so x=5 is not a solution .
- For x=9 we get "9−2=4" which is not true , so x=9 is not a solution .

In this case x = 6 is the only solution.

You might like to practice solving some animated equations .

## More Than One Solution

There can be more than one solution.

## Example: (x−3)(x−2) = 0

When we gather all solutions together it is called a Solution Set

The above solution set is: {2, 3}

## Solutions Everywhere!

Some equations are true for all allowed values and are then called Identities

## Example: sin(−θ) = −sin(θ) is one of the Trigonometric Identities

So it is also true for θ = 90°

Is it true for all values of θ ? Try some values for yourself!

## How to Solve an Equation

There is no "one perfect way" to solve all equations.

## A Useful Goal

But we often get success when our goal is to end up with:

## Example: Solve 3x−6 = 9

and a short calculation reveals that x = 5

## Like a Puzzle

Here are some things we can do:

- Add or Subtract the same value from both sides
- Clear out any fractions by Multiplying every term by the bottom parts
- Divide every term by the same nonzero value
- Combine Like Terms
- Expanding (the opposite of factoring) may also help
- Recognizing a pattern, such as the difference of squares
- Sometimes we can apply a function to both sides (e.g. square both sides)

## Example: Solve √(x/2) = 3

And the more "tricks" and techniques you learn the better you will get.

## Special Equations

There are special ways of solving some types of equations. Learn how to ...

## Check Your Solutions

You should always check that your "solution" really is a solution.

## How To Check

Take the solution(s) and put them in the original equation to see if they really work.

## Example: solve for x:

We have said x≠3 to avoid a division by zero.

Let's multiply through by (x − 3) :

Which can be solved by having x=3

Let us check x=3 using the original question:

Hang On: 3 − 3 = 0 That means dividing by Zero!

And anyway, we said at the top that x≠3 , so ...

x = 3 does not actually work, and so:

"Solving" only gives us possible solutions, they need to be checked!

- Note down where an expression is not defined (due to a division by zero, the square root of a negative number, or some other reason)
- Show all the steps , so it can be checked later (by you or someone else)

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## Equation Word Problems Worksheets

One Step Equation Word Problem Worksheets

Two-Step Equation Word Problems: Integers

Two-Step Equation Word Problems: Fractions and Decimals

MCQ - Two-Step Equation Word Problems

Multi-Step Equation Word Problems: Integers

Multi-step equation Word Problems: Fractions and Decimals

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## Section 2.2 : Linear Equations

Solve each of the following equations and check your answer.

- \(4x - 7\left( {2 - x} \right) = 3x + 2\) Solution
- \(2\left( {w + 3} \right) - 10 = 6\left( {32 - 3w} \right)\) Solution
- \(\displaystyle \frac{{4 - 2z}}{3} = \frac{3}{4} - \frac{{5z}}{6}\) Solution
- \(\displaystyle \frac{{4t}}{{{t^2} - 25}} = \frac{1}{{5 - t}}\) Solution
- \(\displaystyle \frac{{3y + 4}}{{y - 1}} = 2 + \frac{7}{{y - 1}}\) Solution
- \(\displaystyle \frac{{5x}}{{3x - 3}} + \frac{6}{{x + 2}} = \frac{5}{3}\) Solution

## Quadratic Equations: Very Difficult Problems with Solutions

## Online Equation Solver

Solve linear, quadratic and polynomial systems of equations with wolfram|alpha.

## More than just an online equation solver

## Tips for entering queries

- find roots to quadratic x^2-7x+12
- plot inequality x^2-7x+12<=0
- solve {3x-5y==2,x+2y==-1}
- plot inequality 3x-5y>=2 and x+2y<=-1
- solve 3x^2-y^2==2 and x+2y^2==5
- plot 3x^2-y^2>=2 and x+2y^2<=5
- View more examples »

## Access instant learning tools

Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator

## About solving equations

A value is said to be a root of a polynomial if ..

## How Wolfram|Alpha solves equations

## Equation Solver

Enter the Equation you want to solve into the editor.

Please ensure that your password is at least 8 characters and contains each of the following:

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Go to the Equation Plotting page

## Introduction to Equations

Example 1 Consider the equation 2x-1 = x+2

## Math Topics

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## Praxis Core Math

- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example

## Algebraic word problems | Lesson

- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example

## What are algebraic word problems?

- Translating sentences to equations
- Solving linear equations with one variable
- Evaluating algebraic expressions
- Solving problems using Venn diagrams

## How do we solve algebraic word problems?

- Define a variable.
- Write an equation using the variable.
- Solve the equation.
- If the variable is not the answer to the word problem, use the variable to calculate the answer.

## What's a Venn diagram?

- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text
- (Choice A) $ 4 \$4 $ 4 dollar sign, 4 A $ 4 \$4 $ 4 dollar sign, 4
- (Choice B) $ 5 \$5 $ 5 dollar sign, 5 B $ 5 \$5 $ 5 dollar sign, 5
- (Choice C) $ 9 \$9 $ 9 dollar sign, 9 C $ 9 \$9 $ 9 dollar sign, 9
- (Choice D) $ 14 \$14 $ 1 4 dollar sign, 14 D $ 14 \$14 $ 1 4 dollar sign, 14
- (Choice E) $ 20 \$20 $ 2 0 dollar sign, 20 E $ 20 \$20 $ 2 0 dollar sign, 20
- (Choice A) 10 10 1 0 10 A 10 10 1 0 10
- (Choice B) 12 12 1 2 12 B 12 12 1 2 12
- (Choice C) 24 24 2 4 24 C 24 24 2 4 24
- (Choice D) 30 30 3 0 30 D 30 30 3 0 30
- (Choice E) 32 32 3 2 32 E 32 32 3 2 32
- (Choice A) 4 4 4 4 A 4 4 4 4
- (Choice B) 10 10 1 0 10 B 10 10 1 0 10
- (Choice C) 14 14 1 4 14 C 14 14 1 4 14
- (Choice D) 18 18 1 8 18 D 18 18 1 8 18
- (Choice E) 22 22 2 2 22 E 22 22 2 2 22

## Things to remember

Want to join the conversation.

Ask Mathcrave AI Tutor for a clear step-by-step math solutions. Just ask for help!

## Fraction AI Tutor

To obtain the solution for a word problem involving fractions, follow these steps:

## Differentiation

## Solving Quadratic Equations

## Solve simultaneous equation

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## Algebra Calculator

Calculate equations, inequatlities, line equation and system of equations step-by-step.

- One-Step Addition
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## Most Used Actions

- -x+3\gt 2x+1
- (x+5)(x-5)\gt 0
- 10^{1-x}=10^4
- \sqrt{3+x}=-2
- 6+11x+6x^2+x^3=0
- factor\:x^{2}-5x+6
- simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}
- x+2y=2x-5,\:x-y=3

## Frequently Asked Questions (FAQ)

How do you solve algebraic expressions.

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Microsoft Math Solver - Math Problem Solver & Calculator Get step-by-step solutions to your math problems Try Math Solver Type a math problem Solve Quadratic equation x2 − 4x − 5 = 0 Trigonometry 4sinθ cosθ = 2sinθ Linear equation y = 3x + 4 Arithmetic 699 ∗533 Matrix [ 2 5 3 4][ 2 −1 0 1 3 5] Simultaneous equation { 8x + 2y = 46 7x + 3y = 47

Type a math problem Solve algebra trigonometry Get step-by-step explanations See how to solve problems and show your work—plus get definitions for mathematical concepts Graph your math problems Instantly graph any equation to visualize your function and understand the relationship between variables Practice, practice, practice

To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.

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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.

To solve your equation using the Equation Solver, type in your equation like x+4=5. The solver will then show you the steps to help you learn how to solve it on your own. Solving Equations Video Lessons Solving Simple Equations Need more problem types? Try MathPapa Algebra Calculator Show Keypad

Some equations are true for all allowed values and are then called Identities Example: sin (−θ) = −sin (θ) is one of the Trigonometric Identities Let's try θ = 30°: sin (−30°) = −0.5 and −sin (30°) = −0.5 So it is true for θ = 30° Let's try θ = 90°: sin (−90°) = −1 and −sin (90°) = −1 So it is also true for θ = 90° Is it true for all values of θ?

Two-Step Equation Word Problems: Integers Interpret this set of word problems that require two-step operations to solve the equations. Each printable worksheet has five word problems ideal for 6th grade, 7th grade, and 8th grade students. Two-Step Equation Word Problems: Fractions and Decimals

Section 2.2 : Linear Equations Solve each of the following equations and check your answer. 4x−7(2−x) = 3x+2 4 x − 7 ( 2 − x) = 3 x + 2 Solution 2(w+3)−10 = 6(32−3w) 2 ( w + 3) − 10 = 6 ( 32 − 3 w) Solution 4−2z 3 = 3 4 − 5z 6 4 − 2 z 3 = 3 4 − 5 z 6 Solution 4t t2−25 = 1 5 −t 4 t t 2 − 25 = 1 5 − t Solution

Problem 6 sent by Κυριάκος There is a two-digit number whose digits are the same, and has got the following property: When squared, it produces a four-digit number, whose first two digits are the same and equal to the original's minus one, and whose last two digits are the same and equal to the half of the original's.

For equation solving, Wolfram|Alpha calls the Wolfram Language's Solve and Reduce functions, which contain a broad range of methods for all kinds of algebra, from basic linear and quadratic equations to multivariate nonlinear systems.

Equation Solver Step 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result!

Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions. ... Algebra 1. Unit: Solving equations & inequalities. Not feeling ready for this? ... Using inequalities to solve problems Get 3 of 4 questions to level up! Compound inequalities. Learn ...

Solving equations & inequalities > Linear equations with variables on both sides Equations with variables on both sides CCSS.Math: 8.EE.C.7, 8.EE.C.7b Google Classroom Solve for f f. -f+2+4f=8-3f −f + 2+ 4f = 8 − 3f f = f = Stuck? Review related articles/videos or use a hint. Report a problem 7 4 1 x x y y \theta θ \pi π 8 5 2 0 9 6 3 Do 4 problems

An identity is an equation that is satisfied by all numbers from its replacement set. Example 1 Consider the equation 2x-1 = x+2. The replacement set here is the set of all real numbers. The equation is conditional since, for example, 1 is a member of the replacement set but not of the solution set. Example 2 Consider the equation (x-1) (x+1 ...

Given a general quadratic equation of the form ax²+bx+c=0 with x representing an unknown, with a, b and c representing constants, and with a ≠ 0, the quadratic formula is: x= (-b±√ (b²-4ac))/2a where the plus-minus symbol "±" indicates that the quadratic equation has two solutions. Factorization

The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!

Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer.

To obtain the solution for a word problem involving fractions, follow these steps: 1. State the problem clearly. 2. Add the phrase "show me the step-by-step solution" to your question. Simplify fractions without. To simplify fractions without showing the steps, utilize the phrase "solve this fraction" before posing your inquiries.

Learn about solve equations using our free math solver with step-by-step solutions.

How do you solve algebraic expressions? To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.

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