The solution set of the inequation \( |8x-7|\le\displaystyle\frac{2}{3} \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \left[\displaystyle\frac{19}{24},\frac{23}{24}\right] \)
For \( a\gt 0 \), \( |X|\le a \) means \( -a\le X\le a \):
\( \displaystyle -\frac{2}{3}\le 8x-7\le\frac{2}{3} \)
Adding 7 throughout:
\( \displaystyle \frac{19}{3}\le 8x\le\frac{23}{3} \)
Dividing by 8:
\( \displaystyle \frac{19}{24}\le x\le\frac{23}{24} \)
Both end points are included because of “\( \le \)”, so the solution set is the closed interval \( \left[\frac{19}{24},\frac{23}{24}\right] \).