High School

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Solve [tex]|x+4|-5=6[/tex]

A. [tex]x=7[/tex] and [tex]x=-7[/tex]
B. [tex]x=7[/tex] and [tex]x=15[/tex]
C. [tex]x=-7[/tex] and [tex]x=-15[/tex]
D. [tex]x=7[/tex] and [tex]x=15[/tex]

Answer :

To solve the equation [tex]\( |x+4| - 5 = 6 \)[/tex], follow these steps:

1. Isolate the Absolute Value:
[tex]\[
|x+4| - 5 = 6
\][/tex]
Add 5 to both sides to isolate the absolute value:
[tex]\[
|x+4| = 11
\][/tex]

2. Consider the two cases for the absolute value equation [tex]\( |x+4| = 11 \)[/tex]:

- Case 1: [tex]\( x + 4 = 11 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 4 from both sides:
[tex]\[
x = 11 - 4 = 7
\][/tex]

- Case 2: [tex]\( x + 4 = -11 \)[/tex]
- Solve for [tex]\( x \)[/tex] by subtracting 4 from both sides:
[tex]\[
x = -11 - 4 = -15
\][/tex]

Therefore, the solutions for the equation [tex]\( |x+4|-5=6 \)[/tex] are [tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex].

Based on these solutions, the correct choice from the options provided is:
C. [tex]\( x = -7 \)[/tex] and [tex]\( x = -15 \)[/tex]

Please note that the given result matches with option [tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex], but it seems none of the options directly list both. There might be a typo in the provided options.

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