Question

Solve the equation. Graph and check your solutions.
StartAbsoluteValue x EndAbsoluteValue minus 13equalsminus3
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 \( |x| - 13 = -3 \), we can start by isolating the absolute value:

1. Add 13 to both sides:
\[
|x| - 13 + 13 = -3 + 13
\]
\[
|x| = 10
\]

2. Now, we can remove the absolute value. The equation \( |x| = 10 \) can be split into two cases:
- Case 1: \( x = 10 \)
- Case 2: \( x = -10 \)

So, the solutions are:
\[
x = 10 \quad \text{or} \quad x = -10
\]

### Part 1
Select the correct choice and fill in your answer box:

A.
\[ x = 10, -10 \]

### Checking the solutions:
1. For \( x = 10 \):
\[
|10| - 13 = 10 - 13 = -3 \quad \text{(True)}
\]

2. For \( x = -10 \):
\[
|-10| - 13 = 10 - 13 = -3 \quad \text{(True)}
\]

Both solutions check out.

### Graphing the solutions:
To graph \( y = |x| - 13 \) and \( y = -3 \):

- The graph of \( y = |x| - 13 \) is a "V" shape opening upward with its vertex at (0, -13).
- The line \( y = -3 \) is a horizontal line.

The points where these two graphs intersect correspond to the solutions we found earlier, \( x = 10 \) and \( x = -10 \).

Therefore, the final answer is:
\[ x = 10, -10 \]