Answer :
Sure! Let's solve the equation [tex]\( |x+5| - 6 = 7 \)[/tex] step-by-step.
1. Start by isolating the absolute value expression:
[tex]\[ |x+5| - 6 = 7 \][/tex]
Add 6 to both sides to isolate the absolute value:
[tex]\[ |x+5| = 13 \][/tex]
2. The equation [tex]\( |x+5| = 13 \)[/tex] means that the expression inside the absolute value can be either [tex]\( 13 \)[/tex] or [tex]\( -13 \)[/tex]. This gives us two equations to solve:
[tex]\[ x+5 = 13 \][/tex]
[tex]\[ x+5 = -13 \][/tex]
3. Solve the first equation [tex]\( x+5 = 13 \)[/tex]:
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
4. Solve the second equation [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 [tex]\( |x+5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{D. \ x=8 \ \text{and} \ x=-18} \][/tex]
1. Start by isolating the absolute value expression:
[tex]\[ |x+5| - 6 = 7 \][/tex]
Add 6 to both sides to isolate the absolute value:
[tex]\[ |x+5| = 13 \][/tex]
2. The equation [tex]\( |x+5| = 13 \)[/tex] means that the expression inside the absolute value can be either [tex]\( 13 \)[/tex] or [tex]\( -13 \)[/tex]. This gives us two equations to solve:
[tex]\[ x+5 = 13 \][/tex]
[tex]\[ x+5 = -13 \][/tex]
3. Solve the first equation [tex]\( x+5 = 13 \)[/tex]:
Subtract 5 from both sides:
[tex]\[ x = 13 - 5 \][/tex]
[tex]\[ x = 8 \][/tex]
4. Solve the second equation [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 [tex]\( |x+5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{D. \ x=8 \ \text{and} \ x=-18} \][/tex]