Answer :
Sure, I can help with that! Let's solve the equation step-by-step.
We are given the equation:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
To isolate the absolute value expression, we add 6 to both sides of the equation:
[tex]\[ |x + 5| - 6 + 6 = 7 + 6 \][/tex]
[tex]\[ |x + 5| = 13 \][/tex]
Now, we need to consider the two cases for the absolute value [tex]\( |x + 5| \)[/tex]:
Case 1:
[tex]\[ x + 5 = 13 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
Case 2:
[tex]\[ x + 5 = -13 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
Therefore, the solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are:
[tex]\[ x = 8 \][/tex]
[tex]\[ x = -18 \][/tex]
So, the correct answer is:
C. [tex]\( x = 8 \)[/tex] and [tex]\( x = -8 \)[/tex]
We are given the equation:
[tex]\[ |x + 5| - 6 = 7 \][/tex]
To isolate the absolute value expression, we add 6 to both sides of the equation:
[tex]\[ |x + 5| - 6 + 6 = 7 + 6 \][/tex]
[tex]\[ |x + 5| = 13 \][/tex]
Now, we need to consider the two cases for the absolute value [tex]\( |x + 5| \)[/tex]:
Case 1:
[tex]\[ x + 5 = 13 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
Case 2:
[tex]\[ x + 5 = -13 \][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = -13 - 5 \][/tex]
[tex]\[ x = -18 \][/tex]
Therefore, the solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are:
[tex]\[ x = 8 \][/tex]
[tex]\[ x = -18 \][/tex]
So, the correct answer is:
C. [tex]\( x = 8 \)[/tex] and [tex]\( x = -8 \)[/tex]