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

Answer :

Let's solve the equation step-by-step:

The equation given is:
[tex]\[ |x+4| - 5 = 6 \][/tex]

First, let's isolate the absolute value expression by adding 5 to both sides:
[tex]\[ |x+4| = 11 \][/tex]

The expression inside the absolute value, [tex]\( |x+4| = 11 \)[/tex], can result in two possible equations because the absolute value of a number is the number itself if positive, or its opposite if negative. Thus, we have:

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

Now, solve each of these equations for [tex]\( x \)[/tex].

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

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

So the solutions are [tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex].

Checking the options, the correct answer is:
D. [tex]\( x = 7 \)[/tex] and [tex]\( x = -15 \)[/tex]

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