2.
The inequation is given as,
[tex]\lvert4x-5\rvert\leq7[/tex]
Consider the analogy,
[tex]\lvert a\rvert\leq b\Rightarrow-b\leq a\leq b[/tex]
Applying this analogy to the given inequality,
[tex]-7\leq4x-5\leq7[/tex]
Now, we just need to obtain the solution set for this inequality.
Add 5 to each term,
[tex]\begin{gathered} -7+5\leq4x-5+5\leq7+5 \\ -2\leq4x\leq12 \end{gathered}[/tex]
Divide by 4 each term of the inequality,
[tex]\begin{gathered} \frac{-2}{4}\leq\frac{4x}{4}\leq\frac{12}{4} \\ -0.5\leq x\leq3 \end{gathered}[/tex]
Thus, the solution set to the given inequation is obtained as,
[tex]-0.5\leq x\leq3[/tex]
