The given inequality is \( 52 > 8 - \frac{j}{2} \). To isolate the variable term, subtract 8 from both sides:
\[ 52 - 8 > -\frac{j}{2} \]
\[ 44 > -\frac{j}{2} \]
Step 2: Eliminate the fraction
To eliminate the fraction, multiply both sides by -2. Remember to reverse the inequality sign when multiplying by a negative number:
\[ 44 \times -2 < j \]
\[ -88 < j \]
Step 3: Interpret the inequality
The inequality \( -88 < j \) means that \( j \) must be greater than -88.