The solution set for the inequality |5x-3|≤displaystyle1/5 is:

The correct answer is Option (2) → \( \left[\displaystyle\frac{14}{25},\displaystyle\frac{16}{25}\right] \)

For a > 0, \( |t|\le a \) means \( -a\le t\le a \).

    \( \displaystyle -\frac{1}{5}\le 5x-3\le\frac{1}{5} \)

Adding 3 throughout:

    \( \displaystyle \frac{14}{5}\le 5x\le\frac{16}{5} \)

Dividing by 5:

    \( \displaystyle \frac{14}{25}\le x\le\frac{16}{25} \)

So the solution set is the closed interval \( \left[\frac{14}{25},\frac{16}{25}\right] \).

Shortcut: The solution set must contain \( x=\frac{3}{5}=\frac{15}{25} \), where 5x − 3 = 0. Only Option (2) contains it.