Question

which of the following is a solution to the inequality below?
$-8 - \frac{j}{8} < -12$
$j = 112$
$j = -72$
$j = -96$
$j = 8$

Explanation:

Step1: Solve the inequality for \( j \)

Start with the inequality \(-8 - \frac{j}{8} < -12\). First, add 8 to both sides:
\[
-8 - \frac{j}{8} + 8 < -12 + 8
\]
Simplify both sides:
\[
-\frac{j}{8} < -4
\]
Now, multiply both sides by -8. Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign flips:
\[
-\frac{j}{8} \times (-8) > -4 \times (-8)
\]
Simplify both sides:
\[
j > 32
\]

Step2: Check each option

• For \( j = 112 \): \( 112 > 32 \), so this satisfies the inequality.
• For \( j = -72 \): \( -72 < 32 \), does not satisfy.
• For \( j = -96 \): \( -96 < 32 \), does not satisfy.
• For \( j = 8 \): \( 8 < 32 \), does not satisfy.

Answer:

\( j = 112 \)