Question

select the correct answer.

which of the following graphs shows the solution set for the inequality below?

\\(|2x + 2| > 4\\)

Explanation:

Set up the compound inequality

$$ 2x + 2 > 4 \quad \text{or} \quad 2x + 2 < -4 $$

Solve each inequality

$$
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$$

Identify the matching graph

$$ x < -3 \quad \text{or} \quad x > 1 $$

This corresponds to open circles at \(-3\) and \(1\) with arrows pointing outward to the left and right.

Answer:

• (A) Open circles at -1 and 3, arrows pointing outward
• (B) Open circles at -3 and 1, arrows pointing outward (Correct answer)
• (C) Open circle at 1, arrow pointing to the right
• (D) Open circles at -3 and 1, shaded region between them