1. New Jersey Curriculum Standards
4.1 B
4.3 A, B, C
4.5 A, B, C, D

2. Objective Solve equations by using addition and subtraction.
Solve equations by using multiplication and division.

3. Glossary Terms Addition Property of Equality
Subtraction Property of Equality
Division Property of Equality
Multiplication Property of Equality

4. List the Order of Operations
Addition/Subtraction
Multiplication/Division
Exponent
Parenthesis
Parenthesis
Exponent
Multiplication/Division
Addition/Subtraction
In Order to solve for a given variable, turn Order of Operations upside down.

5. Example No. 1
x + 7 12 =
Because 7 is added to x, to find the value of x, subtract 7 -7 -7 x 5 =
Whatever is done to one side of the = sign, must be done to the other side.
Solving equations is a balancing act.

6. Example No. 2
x - 2 -8 =
Because 2 is subtracted from x, to find the value of x, add 2 +2 +2 x -6 =
Whatever is done to one side of the = sign, must be done to the other side.

7. Example No. 3
a + b c =
Because b is added to a, to find the value of b, subtract a -a -a b
c - a =
Whatever is done to one side of the = sign, must be done to the other side.
Solving equations is a balancing act.

8. Example No. 4
-a + b -c =
Because a is subtracted from b, to find the value of b, add a +a +a b
-c + a =
Whatever is done to one side of the = sign, must be done to the other side.

9. Solve by keeping them balanced.
Do These Together
Solve by keeping them balanced. 5. 6.
7 + x = 1
-7 + x = -18
x =
x = -6

10. Solve by keeping them balanced.
Do These Together
Solve by keeping them balanced. 7. 8.
-w + y = -z
w + y = z
-y y
+ w w
w = z - y
y = -z + w

11. Solve by keeping them balanced.
TRY THESE
Solve by keeping them balanced. 9.
10.
X – 12 = -4
-3 = x + 5
= x
X = 8

12. Solve by keeping them balanced.
TRY THESE
Solve by keeping them balanced.
11. 12
x = 0
X – 6 = 6
x = -5
X = 12

13. Solve by keeping them balanced.
TRY THESE
Solve by keeping them balanced.
13.
14.
-y + n = t
a - n = t
+ n n
+ y y
a = t + n
n = t + y

14. Example No. 15
Solve for the given variable
9x = 72
Keep the equation balanced.
The relationship between the coefficient 9 and the variable x is multiplication. To solve for x, divide by the coefficient.
÷ ÷9
x =

15. Example No. 16
Solve for the given variable
Keep the equation balanced.
X = 0.2
*(11)
(11)* 11
The relationship between the 11 and the variable x is division. To solve for x, multiply by the reciprocal.
x =

16. Do These Together x = -0.8 -6x = 42 4* *4 4 ÷-6 ÷ -6 x = -7 x = -3.2
20.
Do These Together
21.
-6x = 42 4*
x = -0.8 *4 4
÷-6 ÷ -6
x = -7
x = -3.2

17. Do These Together x = Z V = I * R Y * * Y Y ÷I ÷ I V = R x = Z Y I
22.
Do These Together
Solve for R
23.
V = I * R
Y *
x = Z
* Y Y
÷I ÷ I
V = R
x = Z Y I
÷Z ÷ Z
x = Y Z

18. TRY THESE 15 = -3b 1.5* 3 = m *1.5 1.5 ÷-3 ÷ -3 -5 = b 4.5 = m 20.3
21.3
15 = -3b
1.5*
3 = m
*1.5
1.5
÷-3 ÷ -3
-5 = b
4.5 = m

19. Divide each side of the equal sign by 5. a = 1080
The sum of the interior angles of a regular pentagon is What is the measure of each angle?
Skill 22
Write an equation to describe the problem.
5a = 5400
÷5 ÷5
Divide each side of the equal sign by 5.
a = 1080

20. In baseball, to compute batting average, use the following formula.
22.2
In baseball, to compute batting average, use the following formula.
Hits
= Average
At Bats
Tina has been at bat 80 times and has a batting average of How many hits did she get?
Multiply by 80.
80 *
Hits
=.3125
* 80 80
Hits = 25

21. 22.3
TRY THESE
22.4
1/6 of an apple pie contains 18 grams of fat. How many grams of fat in the entire pie? Write an equation to describe the situation and solve for the variable.
An 8 foot board costs $3.28. How much does each foot cost? Write an equation to describe the situation and solve for the variable. 6* *6
8x = $3.28
x = 108
x = .41