Question

which of the following graphs shows the complete solution set for the equation below?
$3|x + 3| = 3$

a. two number lines with red dots
and
another number line with a red dot

b. number line with a red dot

c. number line with a red arrow and an open circle

d. number line with two open circles and red arrows

Explanation:

Step1: Isolate absolute value

Divide both sides by 3:
$$|x + 3| = 1$$

Step2: Split into two cases

Case 1: \(x + 3 = 1\)
Case 2: \(x + 3 = -1\)

Step3: Solve Case 1

Subtract 3 from both sides:
$$x = 1 - 3 = -2$$

Step4: Solve Case 2

Subtract 3 from both sides:
$$x = -1 - 3 = -4$$

Step5: Match to graph

The solution set is \(x=-2\) and \(x=-4\), which corresponds to option A's two filled dots on the number lines.

Answer:

A. (The two number lines with filled dots at \(x = -2\) and \(x = -4\))