The Concept of Compound Inequalities

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Compound Inequalities

3-6
Reteaching
A compound inequality with the word or means one or both inequalities must be true. The graph of the compound inequality a < –4 or a ≥ 3 is shown below.

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A compound inequality with the word and means both inequalities must be true. The graph of the compound inequality b ≤ 4 and b > –1 is shown below.

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To solve a compound inequality, solve the simple inequalities from which it is made.

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Problem

What are the solutions of 17 ≤ 2x + 7 ≤ 29? Graph the solutions.

17 ≤ 2x + 7 ≤ 29 is the same as 17 ≤ 2x + 7 and 2x + 7 ≤ 29. You can solve it as two inequalities.

|17 ≤ 2x + 7 |and |2x + 7 ≤ 29 | |17 – 7 ≤ 2x + 7 – 7 |and |2x + 7 – 7 ≤ 29 – 7 | |10 ≤ 2x |and |2x ≤ 22 | |[pic] |and |[pic] | |5 ≤ x |and |x ≤ 11 |

To graph the compound inequality, place closed circles at 5 and 11. Shade between the two circles.

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Prentice Hall Algebra 1 • Teaching Resources
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3-6

Compound Inequalities
Reteaching (continued)
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Problem
What are the solutions of 3t – 5 < –8 or 2t + 5 > 17? Graph the solutions. Solve each inequality.

|3t – 5 < –8 |or |2t + 5 > 17 | |3t – 5 + 5 < –8 + 5 |or |2t + 5 – 5 > 17 – 5 | |3t < –3 |or |2t > 12 | |[pic] |or |[pic] | |t < –1 |or |t >...
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