Question

solve the following absolute value inequality.\\(\frac{|x - 3|}{2} > 1\\)\\(x > ?\\) or \\(x < \square\\)

Explanation:

Step1: Eliminate denominator

Multiply both sides by 2:
$$|x-3| > 2$$

Step2: Split absolute value inequality

For $|A| > B$, split into $A > B$ or $A < -B$:
$$x-3 > 2 \quad \text{or} \quad x-3 < -2$$

Step3: Solve first inequality

Add 3 to both sides:
$$x > 2 + 3 = 5$$

Step4: Solve second inequality

Add 3 to both sides:
$$x < -2 + 3 = 1$$

Answer:

$x > 5$ or $x < 1$