Question

which of the following is a solution to the inequality below?
$-1 - \frac{y}{16} > 3$
$y = 96$ $y = -128$ $y = -48$ $y = 80$

Explanation:

Step1: Solve the inequality for \( y \)

Start with the inequality \(-1 - \frac{y}{16} > 3\). First, add 1 to both sides:
\(-\frac{y}{16} > 3 + 1\)
\(-\frac{y}{16} > 4\)
Then, multiply both sides by -16. Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign changes:
\(y < 4\times(-16)\)
\(y < -64\)

Step2: Check each option

• For \( y = 96 \): \( 96 < -64 \) is false.
• For \( y = -128 \): \( -128 < -64 \) is true.
• For \( y = -48 \): \( -48 < -64 \) is false (since -48 is greater than -64).
• For \( y = 80 \): \( 80 < -64 \) is false.

Answer:

B. \( y = -128 \)