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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]

Sagot :

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

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

2. Split into two cases:
The equation [tex]\( |x+4| = 11 \)[/tex] gives us two separate cases: one in which the expression inside the absolute value is positive, and one in which it is negative.

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

- Case 2:
[tex]\[ -(x + 4) = 11 \][/tex]
Distribute the negative sign:
[tex]\[ -x - 4 = 11 \][/tex]
Add 4 to both sides:
[tex]\[ -x = 15 \][/tex]
Multiply both sides by -1:
[tex]\[ x = -15 \][/tex]

4. Combine the solutions:

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

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