1. Solve One-Step Multiplication and Division Equations

2. Vocabulary
The expression 3x means 3 times the value of x. the numerical factor of a multiplication expression like 3x is called a coefficient. So, 3 is the coefficient of x.

3. Vocabulary
The Division Property of Equality states that the two sides of an equation remain equal when you divide each side by the same nonzero number. If a = b and c ≠ 0, then = The Multiplication Property of Equality states that the two sides of an equation remain equal if you multiply each side by the same number. If a = b, then ac = bc

4. Example 1 Solve: 20 = 4x. Check your solution
20 = 4x write the equation.
20 = 4x division property of equality
4 simplify.
5 = x
Check: 20 = 4x write the original equation
20 = 4(5) replace x with 5
20 = 20 the sentence is true.
So, the solution is 5.

5. Example 2
Solve: -8y = 24. Check your solution -8y = 24 write the equation. -8y = 24 division property of equality -8 = -8 simplify. y = -3 Check: -8y = 24 write the original equation -8(-3) = 24 replace y with = 24 the sentence is true. So, the solution is -3.

6. Practice: Solve each equation. Check your solution 30 = 6x -6a = 36
-9d = -72

7. Example 3
Kyle sent 574 text messages last week. On average, how many messages did he send each day? Let m represent the number of messages Kyle sent. Equation: 574 = 7m write the equation 574 = 7m division property of equality = m simplify. Kyle sent 82 messages on average per day.

8. Example 4
Solve: Check your solution write the equation. multiplication property of equality a = 36 simplify.

9. Practice:
Solve each equation. Check your solution e. f. g.

10. Summary To solve a multiplication equation, use division.
To solve a division equation, use multiplication.
This is called using the inverse of the operation in the equation.