Question
Solve \( -15 \leq 4 x-7 \leq 5 \) a. The answer in interval notation is \( \infty \) (Enter oo for
Ask by Higgins Adkins. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \([-2, 3]\).
Solution
We start with the compound inequality:
–15 ≤ 4x – 7 ≤ 5
Step 1: Add 7 to all three parts to isolate the term containing x:
–15 + 7 ≤ 4x – 7 + 7 ≤ 5 + 7
–8 ≤ 4x ≤ 12
Step 2: Divide each part by 4 to solve for x:
(–8)/4 ≤ x ≤ 12/4
–2 ≤ x ≤ 3
Thus, the solution in interval notation is [–2, 3].
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Simplify this solution Mind Expander
To solve the compound inequality \( -15 \leq 4x - 7 \leq 5 \), start by breaking it into two parts. 1. For \( -15 \leq 4x - 7 \): - Add 7 to both sides to get \( -8 \leq 4x \). - Then, divide by 4 to find \( -2 \leq x \). 2. For \( 4x - 7 \leq 5 \): - Again, add 7 to both sides leading to \( 4x \leq 12 \). - Dividing by 4 yields \( x \leq 3 \). Combining these gives the interval \( -2 \leq x \leq 3 \). In interval notation, this is written as \( [-2, 3] \). So, the final answer in interval notation is: \[ [-2, 3] \]
