Question

question 3 of 10 solve the inequality for x and identify the graph of its solution. |x + 2| < 2 choose the answer that gives both the correct solution and the correct graph. a. solution: x < -4 or x > 0 b. solution: x > -4 and x < 0 c. solution: x < 0 or x > 4 d. solution: x > -4 and x < 0

Explanation:

Step1: Recall absolute - value inequality rule

If \(|a|\lt b\) (\(b > 0\)), then \(-b\lt a\lt b\). Here \(a=x + 2\) and \(b = 2\), so \(-2\lt x+2\lt2\).

Step2: Solve the compound - inequality

Subtract 2 from all parts of the compound - inequality: \(-2-2\lt x+2 - 2\lt2 - 2\).
This simplifies to \(-4\lt x\lt0\), which can be written as \(x>-4\) and \(x < 0\).
The graph of the solution \(x>-4\) and \(x < 0\) is a number line with open circles at \(x=-4\) and \(x = 0\) and the line segment between them shaded.

Answer:

D. Solution: \(x>-4\) and \(x < 0\) (the corresponding graph with open - circles at \(-4\) and \(0\) and the line segment between them shaded)