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 ½.
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
- Always perform the same operation to both sides of the equation.
- When you multiply or divide, you have to multiply and divide by the entire side of the equation.
- Try to perform addition and subtraction first to get some multiple of x by itself on one side.
- Always double check you answer by plugging it back into the original equation.
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
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