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To solve the equation \( |x| + 4 = 7 \), we start by isolating the absolute value:
\[
|x| + 4 = 7
\]
Subtract 4 from both sides:
\[
|x| = 3
\]
The absolute value equation \( |x| = 3 \) means that \( x \) can be either 3 or -3. Therefore, the two values of \( x \) that make the equation true are:
\[
3 \text{ and } -3
\]
Among the responses, the correct answer is:
**3 and -3**