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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], let's go through it step-by-step:

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

2. Solve the Absolute Value Equation:
The equation [tex]\(|x + 4| = 11\)[/tex] means that the expression inside the absolute value, [tex]\(x + 4\)[/tex], can be either 11 or -11 because absolute value represents distance from zero.

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

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

3. Conclusion:
The solutions to the equation are [tex]\(x = 7\)[/tex] and [tex]\(x = -15\)[/tex].

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

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