Parents and Teachers: Support Ducksters by following us on Ducksters Facebook or Ducksters Twitter.
Ducksters Educational SiteDucksters Educational Site
History Biography Geography Science Games

Advertisement

Kids Math

Solving Algebra Equations
with Multiplication and Division

This page assumes you know about variables, basic algebraic equations, and how to solve them using addition and subtraction.

In addition to using addition and subtraction to solve equations, we can also use multiplication and division.

Main Rule

The main rule we need to remember is that when we divide or multiply one side of the equation we have to do the same thing to other side of the equation. We also have to make sure that we divide or multiply the ENTIRE side of the equation and not just a part of it.

Simple Example

We'll take a simple example first:

If 2x = 6, what does x = ?

We can tell by just looking at this that x = 3, however, we can also solve for it. By learning to solve for x, we can then apply this method to more difficult problems where we can't tell the answer just by looking at the equation.

Solving for x

2x = 6

We want to get x by itself on one side of the equation. We can do this by dividing 2x by 2 or multiplying by .

2x (1/2) = 6 (1/2)
(2/2) x = 6/2
x = 3

Let's try a more difficult problem. This time we will need to add and subtract as well.

3x - 6 = 15

It's easiest to do the addition and subtraction steps first with this kind of equation.

add 6 to both sides
(3x - 6) + 6 = (15) + 6
3x = 21

divide both sides by 3
(3x)1/3 = (21)(1/3)

x = 7

Now we should check our answer by plugging in x = 7 back into the original equation:

3x - 6 = 15
3(7) - 6 = 15
21 - 6 = 15
15 = 15

Another Example Problem with 2 Variables

Solve for x in the following equation:

4x + 3y -12 = 24 - y + 2x

Add 12 to both sides

(4x + 3y -12) + 12 = (24 - y + 2x) + 12
(4x + 3y) = (36 - y + 2x)

Subtract 2x from both sides so there is no x on the right side

(4x + 3y) - 2x = (36 - y + 2x) - 2x
(2x + 3y) = (36 - y)

Subtract 3y from both sides so that 2x is alone on one side

(2x + 3y) - 3y = (36 - y) - 3y
(2x) = (36 - 4y)

Divide both sides by 2 so that we get x all alone

(2x)1/2 = (36 - 4y)1/2

x = 18 - 2y

Note that we divided both 36 and 4y by 2 on the right side.

Let's check our answer using the original equation:

4x + 3y -12 = 24 - y + 2x
4(18 - 2y) + 3y -12 = 24 - y + 2(18 - 2y)
72 - 8y + 3y - 12 = 24 - y + 36 - 4y
60 - 5y = 60 - 5y

Things to Remember

More Algebra Subjects
Algebra glossary
Exponents
Linear Equations - Introduction
Linear Equations - Slope Forms
Order of Operations
Ratios
Ratios, Fractions, and Percentages
Solving Algebra Equations with Addition and Subtraction
Solving Algebra Equations with Multiplication and Division

Back to Kids Math

Back to Kids Study


Advertisement


More polls

Advertisement
February is
Black History Month

Learn more about the history of African-Americans at these links

African-American Biographies

African American
Civil Rights
Ads help keep us free. Upgrade to remove.
Ads help keep us free. Upgrade to remove.





About Ducksters Privacy Policy   

Go Ad Free - Remove Ads

Follow us on Ducksters Facebook or Ducksters Twitter

This site is a product of TSI (Technological Solutions, Inc.), Copyright 2017, All Rights Reserved. By using this site you agree to the Terms of Use.