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]
