1. Equations and Inequalities

2. Unit 8 – Solving Multiplication and Division Equations Algebraically

3. Vocabulary
Reciprocal – two numbers whose product is equal to 1. Example: 3 4 𝑎𝑛𝑑 4 3

4. Solving Multiplication Equations Algebraically - Example
Solve algebraically for x , then check.
Solve
12x = 48
x = 4
Check 12x = 48 12(4) = = 48

5. Solving Multiplication Equations Algebraically - Example
Solve algebraically for x , then check.
Solve
15 = 2.5y
y = 6
Check 15 = 2.5y 15 = 2.5(6) 15 = 15

6. Solving Division Equations Algebraically - Example
Solve algebraically for x , then check.
Solve
1 5 z = 3
z =
z = 15
To get rid of the fraction, multiply both sides by the reciprocal. Anytime you multiply a number by its reciprocal the answer is one.
Check 1 5 z = (15) = 3 15 = 15

7. Solving Division Equations Algebraically - Example
Solve algebraically for x , then check.
Solve
𝑟 6 = 11
6 1 𝑟 6 =
r = 66
Check 𝑟 6 = 11 (66) 6 = = 11

8. Solving Multiplication & Division Equations Algebraically - Practice
Solve algebraically, then check.
5y = 75
y = 15
4z = 6.8
z = 1.7
t = 1 4
t = 1 2
9 10 = 5 6 u
u =