Question

solve the inequality. graph the solution |x - 1| < 5 ... the solution is -4 < x < 6 ... graph the solution set on the number line. choose the correct answer below. (options a - f with number lines) help me solve this view an example get more help question 8 of 10 back clear all check answer

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). So for \(|x - 1| < 5\), we apply this rule.
\(-5 < x - 1 < 5\)

Step2: Solve the compound inequality

Add 1 to all parts of the inequality.
\(-5 + 1 < x - 1 + 1 < 5 + 1\)
Simplify each part:
\(-4 < x < 6\)

Answer:

The solution is \(-4 < x < 6\) (and for the graph, it would be an open interval on the number line between -4 and 6, with open circles at -4 and 6 and the line connecting them shaded).