Solve the equation. Graph and check your solutions.

Question

StartAbsoluteValue x EndAbsoluteValue plus 5
equals13
Question content area bottom
Part 1
Solve the equation for x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
xequals
enter your response here
​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)
B.
There is no solution.

Answer 1

To solve the equation |x| + 5 = 13, we need to isolate the absolute value term.

Subtracting 5 from both sides of the equation, we get |x| = 8.

This equation can be split into two separate cases:

Case 1: x ≥ 0
In this case, the equation becomes x + 5 = 13.
Subtracting 5 from both sides, we have x = 8.

Case 2: x < 0
In this case, the equation becomes -x + 5 = 13.
Subtracting 5 from both sides and multiplying by -1, we have x = -8.

Therefore, the solutions to the equation are x = 8 and x = -8.

Graph:

To graph the equation |x| + 5 = 13, we need to plot the points x = 8 and x = -8 on a number line.

Since we have two solutions, we will plot two points on the number line: 8 and -8.
<pre>
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
-8 0 8
</pre>

Check:

We can check the solutions by substituting them back into the original equation |x| + 5 = 13.

For x = 8:
|8| + 5 = 13
8 + 5 = 13
13 = 13 (True)

For x = -8:
|-8| + 5 = 13
8 + 5 = 13
13 = 13 (True)

Therefore, the solutions x = 8 and x = -8 are correct.