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A compound inequality is two simple inequalities joined by the words “and” or “or”.
To solve a compound inequality, first separate it into two inequalities. Determine whether the answer should be a union of sets (“or”) or an intersection of sets (“and”).
Example: n − 2 < −8 or n/8 > 1.
n − 2 < −8 or n/8 > 1.
Either n – 2 < – 8 or n/8 > 1
n < – 6 or n > 8
Example: 3x < 12 or x/3 ≥ 3.
Either 3x < 12 or x/3 ≥ 3
x < 4 or x ≥ 9
Example: −5 ≤ d/3 < 2
−5 ≤ d/3 < 2
– 15 ≤ d < 6
Example: 9x + 9 ≥ −81 and −7 − 9x ≥ −88.
9x + 9 ≥ −81 and −7 − 9x ≥ −88
– 9 – 9 +7 + 7
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9x ≥ – 90 and – 9x ≥ – 81
x ≥ – 10 and x ≤ 9
Example: 5b + 30 ≥ – 25 and – 8b + 15 ≥ -73.
5b + 30 ≥ – 25 and – 8b + 15 ≥ -73
-30 – 30 – 15 – 15
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5b ≥ – 55 and – 8b ≥ – 88
b ≥ -11 and b ≤ 11
Unit 3 Problems and Solutions 3