Answer :
Sure! Let's work through the problem step-by-step.
We need to solve the equation:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
Step-by-Step Solution:
1. Isolate the absolute value expression:
Add 6 to both sides of the equation to isolate the absolute value.
[tex]\[ |x + 5| - 6 + 6 = 7 + 6 \][/tex]
[tex]\[ |x + 5| = 13 \][/tex]
2. Set up two separate equations:
Since the absolute value of a number equals that number or the negative of that number, we need to set up two equations:
[tex]\[ x + 5 = 13 \][/tex]
[tex]\[ x + 5 = -13 \][/tex]
3. Solve each equation:
- For the first equation:
[tex]\[ x + 5 = 13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
- For the second equation:
[tex]\[ x + 5 = -13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
4. Combine the solutions:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are:
[tex]\[ x = 8 \][/tex]
[tex]\[ x = -18 \][/tex]
Answer:
The correct answer is:
[tex]\[ \boxed{A. \ x=8 \ \text{and} \ x=-18} \][/tex]
We need to solve the equation:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
Step-by-Step Solution:
1. Isolate the absolute value expression:
Add 6 to both sides of the equation to isolate the absolute value.
[tex]\[ |x + 5| - 6 + 6 = 7 + 6 \][/tex]
[tex]\[ |x + 5| = 13 \][/tex]
2. Set up two separate equations:
Since the absolute value of a number equals that number or the negative of that number, we need to set up two equations:
[tex]\[ x + 5 = 13 \][/tex]
[tex]\[ x + 5 = -13 \][/tex]
3. Solve each equation:
- For the first equation:
[tex]\[ x + 5 = 13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
- For the second equation:
[tex]\[ x + 5 = -13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
4. Combine the solutions:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are:
[tex]\[ x = 8 \][/tex]
[tex]\[ x = -18 \][/tex]
Answer:
The correct answer is:
[tex]\[ \boxed{A. \ x=8 \ \text{and} \ x=-18} \][/tex]