Question

which of the following is a solution to the inequality below?
$13 \geq \frac{b}{4} - 5$
$b = 56$ $b = 104$ $b = 136$ $b = 116$
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Explanation:

Step1: Solve the inequality for \( b \)

First, add 5 to both sides of the inequality \( 13 \geq \frac{b}{4}-5 \):
\( 13 + 5 \geq \frac{b}{4}-5 + 5 \)
\( 18 \geq \frac{b}{4} \)

Then, multiply both sides by 4 to isolate \( b \):
\( 18\times4 \geq \frac{b}{4}\times4 \)
\( 72 \geq b \)
So \( b \leq 72 \).

Step2: Check each option

• For \( b = 56 \): \( 56 \leq 72 \), so it satisfies \( b \leq 72 \).
• For \( b = 104 \): \( 104>72 \), does not satisfy.
• For \( b = 136 \): \( 136>72 \), does not satisfy.
• For \( b = 116 \): \( 116>72 \), does not satisfy.

Answer:

A. \( b = 56 \)