Question
Solve the equation or inequality. \[ \begin{array}{l}\text { (a) }|b|=7 \\ \text { (b) }|b|<7 \\ \text { (c) }|b|>7 \\ \text { Part } 1 \text { of } 3\end{array} \]
Ask by Rose Cross. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) b = 7 or -7
(b) -7 < b < 7
(c) b < -7 or b > 7
Solution
We are given three problems involving the absolute value of b.
(a) |b| = 7
Recall that |b| = 7 if b equals 7 or -7.
Solution: b = 7 or b = -7
(b) |b| < 7
The inequality |b| < 7 means that the distance from b to 0 is less than 7.
Solution: -7 < b < 7
(c) |b| > 7
Here, |b| > 7 means the distance from b to 0 is greater than 7.
Solution: b < -7 or b > 7
Thus, the answers are as follows:
(a) b = 7 or -7
(b) -7 < b < 7
(c) b < -7 or b > 7
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To solve the equations and inequalities involving absolute values, let’s break each part down. For part (a) \( |b| = 7 \), this means that \( b \) can be either 7 or -7. So, the solutions are: \[ b = 7 \quad \text{or} \quad b = -7. \] For part (b) \( |b| < 7 \), this indicates that the value of \( b \) is between -7 and 7 (not including these endpoints). Therefore, the solution is: \[ -7 < b < 7. \] For part (c) \( |b| > 7 \), this means that \( b \) is either greater than 7 or less than -7. Thus, we have: \[ b < -7 \quad \text{or} \quad b > 7. \]
