Answer :
Certainly! Let's solve the equation step by step:
The equation is [tex]\( |x+5| - 6 = 7 \)[/tex].
1. Isolate the absolute value:
Add 6 to both sides to isolate the absolute value:
[tex]\[
|x+5| = 13
\][/tex]
2. Consider the two cases for the absolute value:
When you have an equation involving absolute value [tex]\( |A| = B \)[/tex], it means:
[tex]\( A = B \)[/tex] or [tex]\( A = -B \)[/tex].
So here, we have:
- Case 1: [tex]\( x + 5 = 13 \)[/tex]
- Case 2: [tex]\( x + 5 = -13 \)[/tex]
3. Solve each case:
- Case 1:
[tex]\[
x + 5 = 13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5 = 8
\][/tex]
- Case 2:
[tex]\[
x + 5 = -13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5 = -18
\][/tex]
4. Conclusion:
The solutions to the equation are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Hence, the correct answer is A. [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
The equation is [tex]\( |x+5| - 6 = 7 \)[/tex].
1. Isolate the absolute value:
Add 6 to both sides to isolate the absolute value:
[tex]\[
|x+5| = 13
\][/tex]
2. Consider the two cases for the absolute value:
When you have an equation involving absolute value [tex]\( |A| = B \)[/tex], it means:
[tex]\( A = B \)[/tex] or [tex]\( A = -B \)[/tex].
So here, we have:
- Case 1: [tex]\( x + 5 = 13 \)[/tex]
- Case 2: [tex]\( x + 5 = -13 \)[/tex]
3. Solve each case:
- Case 1:
[tex]\[
x + 5 = 13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5 = 8
\][/tex]
- Case 2:
[tex]\[
x + 5 = -13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5 = -18
\][/tex]
4. Conclusion:
The solutions to the equation are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Hence, the correct answer is A. [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].