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

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

Answer :

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

1. Isolate the Absolute Value:
Begin by isolating the absolute value expression. We do this by adding 5 to both sides of the equation:
[tex]\[
|x + 4| - 5 + 5 = 6 + 5
\][/tex]
[tex]\[
|x + 4| = 11
\][/tex]

2. Set Up Two Cases:
The absolute value equation [tex]\( |x + 4| = 11 \)[/tex] means there are two possible cases to consider:

- Case 1: [tex]\( x + 4 = 11 \)[/tex]
- Case 2: [tex]\( x + 4 = -11 \)[/tex]

3. Solve Each Case:

- Case 1:
[tex]\[
x + 4 = 11
\][/tex]
Subtract 4 from both sides:
[tex]\[
x = 11 - 4
\][/tex]
[tex]\[
x = 7
\][/tex]

- Case 2:
[tex]\[
x + 4 = -11
\][/tex]
Subtract 4 from both sides:
[tex]\[
x = -11 - 4
\][/tex]
[tex]\[
x = -15
\][/tex]

4. Conclusion:
The solutions to the equation [tex]\( |x + 4| - 5 = 6 \)[/tex] are [tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex].

Thus, the correct answer is A. [tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex].

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