Question

solve the inequality for x and identify the graph of its solution.
3|x + 1| < 6
choose the answer that gives both the correct solution and the correct graph.
a. solution: x > -3 and x < 1
number line with open circles at -3 and 1, red between them
b. solution: x > -3 and x < 1
number line with open circles at -3 and 1, red outside them
c. solution: x < -3 or x > 1
number line with open circles at -3 and 1, red between them
d. solution: x < -1 or x > 3
number line with open circles at -1 and 3, red outside them

Explanation:

Step1: Isolate absolute value

Divide both sides by 3:
$$\frac{3|x+1|}{3} < \frac{6}{3}$$
$$|x+1| < 2$$

Step2: Rewrite without absolute value

For $|A| < b$, $-b < A < b$:
$$-2 < x+1 < 2$$

Step3: Solve for x

Subtract 1 from all parts:
$$-2-1 < x+1-1 < 2-1$$
$$-3 < x < 1$$

Step4: Match to graph

The solution $-3 < x < 1$ corresponds to a number line with open circles at $-3$ and $1$, and the segment between them shaded, which matches option A.

Answer:

A. Solution: $x > -3$ and $x < 1$