Answer :
Let's solve the equation step-by-step:
The equation we have is:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
First, we need to isolate the absolute value expression. We can do this by adding 6 to both sides of the equation:
[tex]\[ |x + 5| = 13 \][/tex]
The equation [tex]\(|x + 5| = 13\)[/tex] means that the expression inside the absolute value, [tex]\(x + 5\)[/tex], can be either 13 or -13. So, we set up two separate equations to solve for [tex]\(x\)[/tex]:
1. [tex]\(x + 5 = 13\)[/tex]
2. [tex]\(x + 5 = -13\)[/tex]
Now, solve each equation:
1. For [tex]\(x + 5 = 13\)[/tex]:
[tex]\[ x + 5 = 13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
2. For [tex]\(x + 5 = -13\)[/tex]:
[tex]\[ x + 5 = -13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
So, the solutions to the equation are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
Therefore, the correct answer choice is:
C. [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex]
The equation we have is:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
First, we need to isolate the absolute value expression. We can do this by adding 6 to both sides of the equation:
[tex]\[ |x + 5| = 13 \][/tex]
The equation [tex]\(|x + 5| = 13\)[/tex] means that the expression inside the absolute value, [tex]\(x + 5\)[/tex], can be either 13 or -13. So, we set up two separate equations to solve for [tex]\(x\)[/tex]:
1. [tex]\(x + 5 = 13\)[/tex]
2. [tex]\(x + 5 = -13\)[/tex]
Now, solve each equation:
1. For [tex]\(x + 5 = 13\)[/tex]:
[tex]\[ x + 5 = 13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
2. For [tex]\(x + 5 = -13\)[/tex]:
[tex]\[ x + 5 = -13 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
So, the solutions to the equation are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
Therefore, the correct answer choice is:
C. [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex]