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

Answer :

Sure, let's solve the equation [tex]\( |x + 4| - 5 = 6 \)[/tex] step by step.

1. Isolate the Absolute Value Expression:

Begin by isolating the absolute value on one side of the equation:

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

Add 5 to both sides:

[tex]\[
|x + 4| = 11
\][/tex]

2. Solve the Absolute Value Equation:

Since the absolute value expression [tex]\( |x + 4| = 11 \)[/tex] means that [tex]\( x + 4 \)[/tex] can be either 11 or -11, we get two separate equations to solve.

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

To solve for [tex]\( x \)[/tex], subtract 4 from both sides:

[tex]\[
x = 11 - 4 = 7
\][/tex]

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

Similarly, solve for [tex]\( x \)[/tex] by subtracting 4 from both sides:

[tex]\[
x = -11 - 4 = -15
\][/tex]

3. Identify the Solutions:

The possible solutions for [tex]\( x \)[/tex] are:

[tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex]

Therefore, the correct answer is option C: [tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex].

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