Answer :
Sure, let's solve the equation [tex]\( |x + 5| - 6 = 7 \)[/tex].
### Step 1: Isolate the Absolute Value
First, we want to isolate the absolute value expression:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
Add 6 to both sides:
[tex]\[ |x + 5| = 13 \][/tex]
### Step 2: Set Up Two Cases for the Absolute Value
The absolute value equation [tex]\( |x + 5| = 13 \)[/tex] can be split into two separate cases:
1. Positive Case: [tex]\( x + 5 = 13 \)[/tex]
2. Negative Case: [tex]\( x + 5 = -13 \)[/tex]
### Step 3: Solve Each Case
Positive Case:
[tex]\[ x + 5 = 13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
Negative Case:
[tex]\[ x + 5 = -13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
### Conclusion
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
So, the correct choice is:
A. [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex]
### Step 1: Isolate the Absolute Value
First, we want to isolate the absolute value expression:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
Add 6 to both sides:
[tex]\[ |x + 5| = 13 \][/tex]
### Step 2: Set Up Two Cases for the Absolute Value
The absolute value equation [tex]\( |x + 5| = 13 \)[/tex] can be split into two separate cases:
1. Positive Case: [tex]\( x + 5 = 13 \)[/tex]
2. Negative Case: [tex]\( x + 5 = -13 \)[/tex]
### Step 3: Solve Each Case
Positive Case:
[tex]\[ x + 5 = 13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
Negative Case:
[tex]\[ x + 5 = -13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
### Conclusion
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
So, the correct choice is:
A. [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex]