Question

solve the following absolute value inequality.\\(\frac{3|x - 1|}{4} < 6\\)\\(x < ?\\) and \\(x > \square\\)

Explanation:

Step1: Eliminate denominator

Multiply both sides by 4.
$$3|x-1| < 24$$

Step2: Isolate absolute value

Divide both sides by 3.
$$|x-1| < 8$$

Step3: Rewrite without absolute value

For $|A| < b$, $-b < A < b$.
$$-8 < x-1 < 8$$

Step4: Solve for x

Add 1 to all parts.
$$-8+1 < x < 8+1$$
$$-7 < x < 9$$

Answer:

$x < 9$ and $x > -7$