Problem

Solve the absolute value inequality.
\[
|4(x-1)+10| \leq 26
\]

Answer

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Answer

The solution to the original inequality is the intersection of the solutions to these two inequalities. Therefore, the solution is -8 ≤ x ≤ 5.

Steps

Step 1 ：First, we remove the absolute value from the inequality |4(x-1)+10| ≤ 26. This gives us two inequalities: 4(x-1)+10 ≤ 26 and -(4(x-1)+10) ≤ 26.

Step 2 ：Solving the first inequality, 4(x-1)+10 ≤ 26, we find that x ≤ 5.

Step 3 ：Solving the second inequality, -(4(x-1)+10) ≤ 26, we find that x ≥ -8.

Step 4 ：The solution to the original inequality is the intersection of the solutions to these two inequalities. Therefore, the solution is -8 ≤ x ≤ 5.

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