S.Gast MIS Fall 2007 1

Solving Variable EquationsA lesson by Mrs. Gast

S.Gast MIS Fall 2007 2

An equation is a mathematical sentence that contains an equals sign. An equals

sign means that both sides of the equation have the same quantity.

A variable is a letter or symbol which represents a number.

S.Gast MIS Fall 2007 3

Here’s an example of an equation using models to demonstrate.

7 = 5 + 2

=

S.Gast MIS Fall 2007 4

7 = 5 + 2

=

Key to Remember:What you do to one side of an equation, you must do to the other side in order

for the equation to stay true.

7-1 = 5 + 2 -1

S.Gast MIS Fall 2007 5

Variables in EquationsHere are some examples of variables in equations:

3 + m = 15 x – 12 = 20 8n = 128 y ÷ 12 = 4

Keys to Remember When solving Variable Equations:

1) Isolate the variable. 2) Balance each side: what you do to one side of the equation, do to the other side.

3) Check to see if the equation is true.

S.Gast MIS Fall 2007 6

Let’s solve an addition variable equation.

3 + m = 15

-3 -3

0

m = 12

Check your answer!

3 + 12 = 15

By subtracting 3 from each side, you are isolating the variable which then gives

your answer. Check your answer by substituting the answer in place of the variable. You have the solution if the equation is true.

S.Gast MIS Fall 2007 7

Let’s solve a subtraction variable equation.

x – 12 = 20

+12 +12

0

x = 32

Check your answer!

32 – 12 = 20

By adding 12 to each side, you are isolating the

variable which then gives your answer.

Check your answer by substituting the answer in place of the variable. You have the solution if the equation is true.

S.Gast MIS Fall 2007 8

Let’s solve a multiplication variable equation.

By dividing each side by 8, you are isolating the variable which

then gives your answer. Check your answer by substituting the answer in place of the variable. You have the solution if the equation is true.

8n = 128 8 8

n = 16

Check your answer! 8 x 16 = 128

S.Gast MIS Fall 2007 9

Let’s solve a division variable equation.

By multiplying each side by 12, you are isolating the variable which then gives

your answer. Check your answer by substituting the answer in place of the variable. You have the solution if the equation is true.

y ÷ 12 = 4 x 12 x 12

y = 48

Check your answer! 48 ÷ 12 = 4

S.Gast MIS Fall 2007 10

My Turn to Make Equations!Don’t forget to

line up your equals sign. 1. c + 13 = 25

2. d - 64 = 29

3. 6 x n = 72

4. y ÷ 5 = 9

Keys to Remember When solving Variable Equations:

1) Isolate the variable. 2) Balance each side: what you do to one side of the equation, do to the other side.

3) Check to see if the equation is true.