The solution set of the inequation \(|2x - 3| \le 4\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\left[-\frac{1}{2}, \frac{7}{2}\right]\)
For \(a \gt 0\), \(|u| \le a\) means \(-a \le u \le a\). So
\(-4 \le 2x - 3 \le 4\)
Adding 3 throughout:
\(-1 \le 2x \le 7\)
Dividing by 2:
\( \displaystyle -\frac{1}{2} \le x \le \frac{7}{2} \)
The solution set is \(\left[-\frac{1}{2}, \frac{7}{2}\right]\).