Page 170 - Math Course 1 (Book 1)

Inequalities: Multiplication and Division

Mo. 5

Lesson 5
Let’s Begin

KEY CONCEPTS:
1. Solve inequalities by multiplying or
dividing by a positive number. Multiply or Divide by a Positive
2. Solve inequalities by multiplying or Number
dividing by a negative number.
Examples

MO. 5 - L5a
Solve 9x ≤ 54. Check your solution.
Solving Inequalities: 9x ≤ 54 Write the inequality.
Multiplication and Division
9x 54
< Divide each side by 9.
9 9
Key Concept x ≤ 6 Simplify.

The solution is x ≤ 6. You can
Multiplication and Answer check this solution by substituting
Division Properties 6 or a number less than 6 into the
inequality.
Words When you multiply or divide each side
of an inequality by the same positive
number, the inequality remains true. d
Solve > 4. Check your solution.
Symbols For all numbers a, b, and c, where c > 0. 9
a b d
1. if a > b, then ac > bc and > > 4 Write the inequality.
c c 9
a b
1. if a < b, then ac < bc and <
c c 9 d > ( 9 ) 4 Multiply each side
Examples 2 < 6 3 > -9 9 by 9.
3 -9 d > 36 Simplify.
4(2) < 4(6) >
3 3
8 < 24 1 > - 3
These properties are also true for a > b and a < b The solution is d > 36. You can
Words When you multiply or divide each side Answer check this solution by substituting
36 or a number greater than 36 into
of an inequality by the same negative the inequality.
number, the inequality symbol must be
reversed for the inequality to remain
true. Standardized Test Example
Symbols For all numbers a, c, and b, and c, where
c < 0. Martha earns $9 per hour working at a fast food
restaurant. Which inequality can be used to f nd
a b
1. if a > b, then ac < bc and < how many hours she must work in a week to earn
c c at least $117?
a b
2. if a < b, then ac > bc and >
c c
Examples 7 > 1 -4 > 16

-2(7) < -2(1) Reverse the -4 > 16
symbols -4 -4 A. 9x < 117
-14 < -2 1 > - 4 B. 9x ≥ 117
These properties are also true for a > b and a < b C. 9x > 117
D. 9x ≤ 117
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