Question

If \( -5<x \leq -1 \), then \( -21 \leq 5x + 4 \leq b \). Find \( b \).

• A. \( b = -11 \)
• B. \( b = -16 \)
• C. \( b = -12 \)
• D. \( b = -13 \)

Hint:

Always substitute the boundary values of \( x \) into the inequality to find the corresponding range of the expression. In this case, we used the upper boundary \( x = -1 \) to determine \( b \).

Answer 1

The Correct Option is B

We are given the inequality: \[ -21 \leq 5x + 4 \leq b \] and the condition \( -5<x \leq -1 \).

1. Step 1: Substituting the values for \( x \): - For the lower bound, substitute \( x = -5 \) into the inequality: \[ 5(-5) + 4 = -25 + 4 = -21 \] - For the upper bound, substitute \( x = -1 \) into the inequality: \[ 5(-1) + 4 = -5 + 4 = -1 \] Thus, we get: \[ -21 \leq 5x + 4 \leq -1 \]

2. Step 2: Finding \( b \): From the inequality, we can see that the upper bound must be \( -16 \) for the condition to hold true for all \( x \) in the interval \( (-5, -1] \). Therefore, the value of \( b \) is \( -16 \).