To solve the inequality [tex]\( \frac{j}{4} - 8 < 4 \)[/tex], follow these steps:
1. Isolate the term with [tex]\( j \)[/tex]:
Add 8 to both sides of the inequality:
[tex]\[
\frac{j}{4} - 8 + 8 < 4 + 8
\][/tex]
Simplifying the left and right sides, we get:
[tex]\[
\frac{j}{4} < 12
\][/tex]
2. Solve for [tex]\( j \)[/tex]:
Multiply both sides of the inequality by 4 to eliminate the denominator (since multiplying or dividing by a positive number doesn't change the direction of the inequality):
[tex]\[
\left( \frac{j}{4} \right) \times 4 < 12 \times 4
\][/tex]
Simplifying this, we obtain:
[tex]\[
j < 48
\][/tex]
Therefore, the best answer is:
D. [tex]\( j < 48 \)[/tex]
