Solve the equation. Graph and check your solutions.
StartAbsoluteValue x EndAbsoluteValue plus 5
equals13
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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.
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.