Unit 07 · Equations Inequalities and RelationshipsLesson

Day 099Testing Inequality Solutions

Standards 6.EE.B.56.EE.B.8

LEARNING TARGET

I can test values and explain the many solutions of an inequality.

01 · LEARN

Build the idea

Substitute each value and decide whether the comparison is true. A continuous number-line ray represents infinitely many real-number solutions. A real situation may restrict useful solutions to whole numbers.

WORKED EXAMPLE 1

Which values in {8, 9, 10} satisfy x ≤ 9? Test each by substitution.

8, 9

Values below 9 work; the endpoint works too.

WORKED EXAMPLE 2

Which values in {10, 11, 12} satisfy x ≤ 11? Does the real-number inequality have only these solutions? Explain.

10, 11; no, infinitely many real values satisfy it

Values below 11 work; the endpoint works too.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

Which values in {10, 11, 12} satisfy x < 11? Test each by substitution.
Which values in {5, 6, 7} satisfy x ≤ 6? Test each by substitution.
Which values in {8, 9, 10} satisfy x < 9? Test each by substitution.
Which values in {3, 4, 5} satisfy x ≤ 4? Test each by substitution.
Which values in {9, 10, 11} satisfy x < 10? Test each by substitution.
Which values in {14, 15, 16} satisfy x ≤ 15? Test each by substitution.
Which values in {7, 8, 9} satisfy x < 8? Does the real-number inequality have only these solutions? Explain.
Which values in {5, 6, 7} satisfy x ≤ 6? Does the real-number inequality have only these solutions? Explain.
Which values in {9, 10, 11} satisfy x < 10? Does the real-number inequality have only these solutions? Explain.
Which values in {14, 15, 16} satisfy x ≤ 15? Does the real-number inequality have only these solutions? Explain.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key

10
Values below 11 work; the endpoint does not work.
5, 6
Values below 6 work; the endpoint works too.
8
Values below 9 work; the endpoint does not work.
3, 4
Values below 4 work; the endpoint works too.
9
Values below 10 work; the endpoint does not work.
14, 15
Values below 15 work; the endpoint works too.
7; no, infinitely many real values satisfy it
Values below 8 work; the endpoint does not work.
5, 6; no, infinitely many real values satisfy it
Values below 6 work; the endpoint works too.
9; no, infinitely many real values satisfy it
Values below 10 work; the endpoint does not work.
14, 15; no, infinitely many real values satisfy it
Values below 15 work; the endpoint works too.

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