1. Multiplication and Division
One-Step Equations
Multiplication and Division
January 3, 2018

2. One-Step Equations Review
To solve an equation, we must get the variable by itself on one side of the equal sign.
Solving equations is like keeping a scale balanced –
whatever is done to one side of the equation must be done to the other side.

3. Division Property of Equality
One-Step Equations
Key Concept
Division Property of Equality
If you divide each side of an equation by the same nonzero number, the two sides remain equal.
Arithmetic
6 = 6
6 6
3 = 3
2 = 2
Algebra
2X = 6
2X 6
2 = 2
X = 3
Example

4. One-Step Equations More Examples 1.) 3X = -9 3X = -9 3 3 X = -3
X = -3
2.) 24 = -8X
24 = -8X
-8 -8
-3 = X

5. One-Step Equations Try these. Write the middle step and solve.
a. ) 4X = -16
b.) -1X = 9
c.) 7 = 4X
d.) 12X = 3
4X ÷ 4 = -16 ÷ 4
-1X ÷ -1 = 9 ÷ -1
7 ÷ 4 = 4X ÷ 4
12X ÷ 12 = 3 ÷ 12
X = -4
X = -9
1 ¾ = X
X = ¼

6. Multiplication Property of Equality
One-Step Equations
Key Concept
Multiplication Property of Equality
If you multiply each side of an equation by the same number, the two sides remain equal.
Algebra
X = -6 2
X2 = -62
X = -12
Arithmetic
5 = 5
52 = 52
10 = 10
Example

7. One-Step Equations Try these. Write the middle step and solve.
a.) X÷3 = 9
b.) X ÷ -4 = 7
c.) X ÷ 3 = -1
d.) 4 = X ÷ 4
X ÷ 3•3 = 9•3
X ÷ -4•-4 = 7•-4
X ÷ 3•3 = -1•3
4•4 = X ÷ 4•4
X = 27
X =-28
X = -3
16 = X

8. Copy and solve the following equations.
4X = 15
X ÷ 2 = -8
9 - X = -1
-12 + X = 0
-X ÷ 3 = 4
X + 5 = 5
X - 4 = 4
-X = 5
X =-50
X ÷ 5 = -55
x = x = 0
x = x = 8
x = x = -5
x = x = -100
x = x = -275