1. Equations #1 12 – 3 = 9 Numerical 3a = 30 Algebraic
An equation is a mathematical statement that
shows 2 quantities are equal. An equation
contains an equal sign.
12 – 3 = 9 Numerical
3a = 30 Algebraic
To solve any equation use inverse operations.
Your goal is to get the variable all by itself.

2. SOLUTION Example: 3a = 30 a = 10 10 is the solution #2
A solution is the final answer to an
equation, or the value of the variable.
Example: 3a = 30
a = is the solution

3. To Solve An Addition Equation#3
Subtract the same number from both sides.
m + 8 = 12
Get the variable alone.
– –8
Subtract 8 from both sides.
m = 4
+8 and -8 cancel each other out.
4 + 8 = 12
Show your check.
12 = 12
Finish your check!

4. To Solve a Subtraction Equation#4
Add the same number to both sides.
a – 15 = 22
Get the variable alone.
Add 15 to both sides.
+15 and -15 cancel out
a = 37
= 22
Show your check!
Finish your check!
22 = 22

5. To Solve a Multiplication Equation#5
To Solve a Multiplication Equation
Divide the same number into both sides
5x = 40
Get the variable alone.
Divide 5 into both sides.
x = 8
5 divided by 5 cancels out to 1.
5 • 8 = 40
Show your check!
40 = 40
Finish your check!

6. To Solve a Division Equation#6
To Solve a Division Equation
Multiply the same number to both sides
x 2
= 20
Get the variable alone.
= 20
2• •2
x 2
Multiply both sides by 2.
2 divided by 2 cancels out to 1.
x = 40
Show your check!
Finish your check!
20 = 20

7. #7 + -3 + -3 a = 18 18 - -3 = 21 21 = 21 Integer Equation
Use inverse operations to solve integer equations.
Get the variable alone.
a – -3 = 21
Add -3 to both sides.
+ -3 and – -3 cancel out
a = 18
= 21
Check your answer
21 = 21
Finish your check

8. Integer Multiplication Equation#8
Integer Multiplication Equation
Divide the same number into both sides
-8x = -64
Get the variable alone.
Divide -8 into both sides.
x = 8
-8 divided by -8 cancel out to 1.
Check your answer.
-8 8 = -64
-64 = -64
Finish your check.

9. Algebra Tile Equations#9
2x = 4
+ +
Draw a picture. + x = + + x
Take away 2 from both sides.
Algebra
2x = 4
-2 = -2
Divide both sides in half.
2x = 2
x = 1

10. Algebra Balance Scales
#10
2x = 3x ) Draw a picture. x x
2) Take away 2x
from both sides. = x x
+ +
3) Take away 4
from both sides. x
Algebra
2x = 3x + 4
-2x = -2x
6 = 1x + 4
2 = x

11. #11
Solve 2 Step Equations
1) Undo the addition or subtraction operation first, by using inverse operations.
2) Undo the multiplication or division second, by using inverse operations.

12. 2 Step Subtract/Multiply Equation
#12
3m - 10 = 17
Get the variable alone.
Add 10 to both sides.
__ __
3m = 27
+10 and -10 cancel out
Divide both sides by 3
m = 9
3 divided by 3 cancel to 1
3(9) – 10 =17
Show your check.
27 – 10 =17
Finish your check.
17 =17

13. 2 Step ADD/DIVIDE Equation
#13
2 Step ADD/DIVIDE Equation
x 2
+ 6 = 14
Get the variable alone.
Subtract 6 from both sides.
x 2
= 8
+ 6 and -6 cancel out.
x 2
Multiply both sides by 2.
( ) = 2 2
2 divided by 2 cancels out
x = 16 16 2
Show your check.
+ 6 = 14
8 + 6 = 14
Finish your check.
14 = 14

14. Rules for Solving Equations
#14
Rules for Solving Equations
1) Goal: Isolate the variable.
2) Undo operations with their opposite operation.
3) Always do the same thing to both sides of the equation.
4) Easiest to undo add/subtract
before multiply/divide.

15. Solve Multi Step Equations
#15

16. Multiple Step Equations
#16
Multiple Step Equations
3x + 4 = 5x - 10
Steps
-3x x
1) Get all of the x’s on 1 side.
4 = 2x - 10
2) Subtract 3x from both
sides.
3) Add 10 to both sides.
14 = 2x
4) Divide both sides by 2
7 = x

17. Negative Coefficient Equations
#17
Negative Coefficient Equations
3 - 2x = 11
1)Get the variable alone, even if the coefficient is negative.
- 2x = 8
__ __
2)Subtract 3 from both sides.
3) +3 and -3 cancel out
x = -4
4) Divide both sides by - 2
3 - 2(-4) = 11
5) -2 divided by –2 cancel out
= 11
6) Show your check.
11 = 11
7) Finish your check.

18. Move the smaller number of x’s to one side
#18
Variable on Both Sides Picture
2x = 4x – 2 – x
+ + x x ++ –
+ + = x x x
2x = 4x - 2
-2x x
Move the smaller number of x’s to one side
2 = 2x - 2
4 = 2x
2 = x

19. Steps To Solve Equations
#19
Get rid of the parenthesis by distributing
Combine like terms
Move the smaller number of x’s to one side
Move all numbers to the other side
Get x all by itself
Check your answer in the original equation
Circle answer. Show work in the check!

20. Equations With Parenthesis
#20
Equations With Parenthesis
5(m - 6) = 10
Get rid of parenthesis first by distributing.
5m - 30 = 10
5m = 40
Check in
the
original
equation! Do
PEMDAS
in the
check!
m = 8
5(8 - 6) = 10
5(2) = 10
10 = 10 

21. Variable On Both Sides Get rid of the parenthesis.
#21
8x - 4 = 3(2x + 8)
Get rid of the parenthesis.
8x - 4 = 6x
+ 24
Get the variables on one side.
-6x x
Subtract 6x from both sides.
2x - 4 = 24
6x and –6x cancel out
2x = 28
__ __
Add 4 to both sides.
Divide both sides by 2.
x = 14
8(14) - 4 = 3(2 14+8)
Show your check!
= 3(36)
Finish your check!
108 = 108

22. Extra

23. Equations #1
An equation is a mathematical statement that shows 2 quantities are equal. An equation contains an equal sign.
12 – 3 = 9 Numerical
3a = 30 Algebraic

24. To Solve a Fraction Equation#7
Multiply both sides by the reciprocal of the fraction.
Multiply the numerators. Multiply the denominators.
Simplify

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