Question

solve each absolute value inequality and show its solution set on a number line. |3 - x| < 5

Explanation:

Step1: Remove absolute value

$$-5 < 3 - x < 5$$

Step2: Subtract 3 from all parts

$$-5 - 3 < 3 - x - 3 < 5 - 3$$
$$-8 < -x < 2$$

Step3: Multiply all parts by -1 (reverse inequalities)

$$8 > x > - 2$$
$$-2 < x < 8$$

Answer:

The solution set is \(-2 < x < 8\). On a number line, it is represented by an open circle at \(-2\) and \(8\) and a line connecting them.