Page 32 - Math Course 3 (Book 1)

More Absolute Value Inequalities

Real World Example Solve |p – 5| < –2.

The average annual rainfall in A. {p | p ≤ –2}
California for the last 100 years is B. {p | p < –2}
23 inches. However, the annual C. {p | p < 3}
rainfall can differ by 10 inches from the 100 year D. Ø
average. What is the range of annual rainfall for
California?
Answer
The difference between the actual rainfall and the
average is less than or equal to 10. Let x be the
actual rainfall in California. Then |x – 23| ≤ 10.

Case 1 Case 2
x – 23 ≤ 10 –(x – 23) ≤ 10 Solve an Absolute Value Inequality (>)
x – 23 + 23 ≤ 10 + 23 x – 23 ≥ –10 Solve |2m – 2| > 6. Then graph the solution set.

x ≤ 33 x – 23 + 23 ≥ –10 + 23
x ≥ 13 A. {m | m > –2 or m < 4}.

The range of rainfall in
Answer
California is {x |13 < x < 33}. B. {m | m > –2 or m > 4}.

Your Turn! C. {m | –2 < m < 4}.

Solve an Absolute Value Inequality (<)
Solve |p + 4| < 6. Then graph the solution set. D. {m | m < –2 or m > 4}.

A. {p | p < 2}

B. {p | p > –10} Answer

C. {p | –10 < p < 2}
Solve |5x – 1| ≥ –2.

D. {p | –2 < p < 10} A. {x | x ≥ 0}
B. {x | x ≥ –5}
C. {x | x is a real number}
D. Ø

Answer
Answer

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