Question

solve the inequality. then graph the solution set and write it in interval notation. |x| + 1 ≤ 5
a. the solution set is (simplify your answer. type your answer in interval notation. use integers or fractions for any numbers in the expression.)
b. the solution set is one or two points. the solution set is { } (type an integer or a fraction. use a comma to separate answers as needed.)
c. the solution set is ∅.
choose the correct graph below.

Explanation:

Step1: Isolate the absolute - value

Subtract 1 from both sides of the inequality \(|x| + 1\leq5\).
\(|x|\leq5 - 1\), so \(|x|\leq4\).

Step2: Solve the absolute - value inequality

If \(|x|\leq4\), then \(-4\leq x\leq4\). In interval notation, the solution set is \([-4,4]\).

Step3: Analyze the graph

The graph of the solution set \([-4,4]\) on a number line will have closed - circles at \(x=-4\) and \(x = 4\) and a line segment connecting them.

Answer:

The solution set is \([-4,4]\). The correct graph is the one with closed - circles at \(-4\) and \(4\) and a line segment between them (you need to visually identify this among the given graph options).