Question

Solve and graph the equation.
StartAbsoluteValue x EndAbsoluteValueequals8
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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 \( |x| = 8 \), we need to understand what the absolute value represents. The absolute value of \( x \) is equal to 8 if either:

1. \( x = 8 \)
2. \( x = -8 \)

Thus, the solutions to the equation \( |x| = 8 \) are:

\[ x = 8 \quad \text{and} \quad x = -8 \]

So the correct choice is:

A.
\( x = 8, -8 \)

Now, let's graph the solution. On a number line:

- Mark the point \( 8 \) with a dot.
- Mark the point \( -8 \) with a dot.

Both points are included in the solution set since the original equation allows for \( x \) to equal both 8 and -8.

In summary, the answer is:
A.
\( x = 8, -8 \)