Using a number line explain why multiplying or dividing by a negative number causes the direction of inequality to flip. Namely explain why −x > −5 becomes x < 5. 2. Explain how you obtain the solution to the compound inequality (using a num- ber line) x − 1 ≤ 3x + 4 ≤ x + 1 3. What is the solution to |3x − 4| ≤ 5 and to |3x − 4| ≥ 5. Plot both solutions on a

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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ISBN:9780079039897
Author:Carter
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Chapter5: Linear Inequalities
Section5.3: Solving Multi-step Inequalities
Problem 64PFA
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1. Using a number line explain why multiplying or dividing by a negative number
causes the direction of inequality to flip. Namely explain why −x > −5 becomes
x < 5.

2. Explain how you obtain the solution to the compound inequality (using a num-
ber line) x − 1 ≤ 3x + 4 ≤ x + 1

3. What is the solution to |3x − 4| ≤ 5 and to |3x − 4| ≥ 5. Plot both solutions on a
number line and comment on any interesting observations you can make.

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