Question
Solve the equation or inequality. Write the solution set to (a) \( |b|=2 \) (b) \( |b|<2 \) (c) \( |b|>2 \)
Ask by Bowers Bowen. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) b = -2 or b = 2
(b) -2 < b < 2
(c) b < -2 or b > 2
Solution
We are given absolute value expressions and need to solve the equation/inequalities for b.
(a) |b| = 2
The absolute value equals 2 if b is 2 or -2.
Solution: b = 2 or b = -2.
(b) |b| < 2
The inequality |b| < 2 means that the distance from b to 0 is less than 2. This implies b lies between -2 and 2.
Solution: -2 < b < 2.
(c) |b| > 2
The inequality |b| > 2 means that b is more than 2 units away from 0. This occurs when b is either less than -2 or greater than 2.
Solution: b < -2 or b > 2.
Thus, the solution sets are:
(a) { -2, 2 }
(b) (-2, 2)
(c) (-∞, -2) ∪ (2, ∞)
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Simplify this solution Mind Expander
For the equation \( |b|=2 \), the solutions are \( b=2 \) and \( b=-2 \). These solutions come from the definition of absolute value, which indicates that the distance from \( b \) to 0 is 2, allowing both positive and negative values.
For the inequality \( |b|<2 \), the solution set is \( -2
