Question

Solve the equation. Graph and check your solutions.
negative 3 StartAbsoluteValue x EndAbsoluteValueequalsnegative 6
Question content area bottom
Part 1
Select the correct choice​ and, if​ necessary, fill in the answer box in your choice below.
A.
xequals
  
enter your response here
​(Simplify your answer. Use a comma to separate answers as​ needed.)
B.
There is no solution.

Answer 1

To solve the equation \(-3 |x| = -6\), we first isolate the absolute value expression.

1. Divide both sides of the equation by -3 to get:
\[
|x| = 2
\]

2. The absolute value equation \( |x| = 2 \) implies that:
\[
x = 2 \quad \text{or} \quad x = -2
\]

Thus, the solutions are:
\[
x = 2, -2
\]

### Part 1 Answer:

The correct choice is:
A.
\( x = 2, -2 \)

### Graphing to Check Solutions:

To check these solutions, we can graph \( y = -3 |x| \) and see where it intersects with \( y = -6 \).

1. The equation \( y = -3 |x| \) is a V-shaped graph facing downward with its vertex at the origin (0,0). It will intercept the horizontal line \( y = -6 \) at the points \( x = 2 \) and \( x = -2 \).

Thus, the solutions \( x = 2 \) and \( x = -2 \) are verified by the graph.

### Summary:
The solutions are \( x = 2, -2 \), and they have been confirmed by both analytical solving and graphical intersection.