Answer :
Sure! Let's solve the equation step-by-step:
We have the equation:
[tex]\[ |x - 4| + 6 = 17 \][/tex]
First, we need to isolate the absolute value:
[tex]\[ |x - 4| = 17 - 6 \][/tex]
[tex]\[ |x - 4| = 11 \][/tex]
Next, we need to solve the absolute value equation. Recall that if [tex]\(|A| = B\)[/tex], then [tex]\(A = B\)[/tex] or [tex]\(A = -B\)[/tex]. Therefore:
[tex]\[ x - 4 = 11 \][/tex]
or
[tex]\[ x - 4 = -11 \][/tex]
Now solve these two simple equations:
1. For [tex]\(x - 4 = 11\)[/tex]:
[tex]\[ x - 4 = 11 \][/tex]
[tex]\[ x = 11 + 4 \][/tex]
[tex]\[ x = 15 \][/tex]
2. For [tex]\(x - 4 = -11\)[/tex]:
[tex]\[ x - 4 = -11 \][/tex]
[tex]\[ x = -11 + 4 \][/tex]
[tex]\[ x = -7 \][/tex]
So, the solutions are [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex].
Looking at the given choices:
A. [tex]\(x = -15\)[/tex] and [tex]\(x = -7\)[/tex]
B. [tex]\(x = -15\)[/tex] and [tex]\(x = 7\)[/tex]
C. [tex]\(x = 15\)[/tex] and [tex]\(x = -15\)[/tex]
D. [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex]
The correct answer is:
[tex]\[ \boxed{D. \, x = 15 \text{ and } x = -7} \][/tex]
We have the equation:
[tex]\[ |x - 4| + 6 = 17 \][/tex]
First, we need to isolate the absolute value:
[tex]\[ |x - 4| = 17 - 6 \][/tex]
[tex]\[ |x - 4| = 11 \][/tex]
Next, we need to solve the absolute value equation. Recall that if [tex]\(|A| = B\)[/tex], then [tex]\(A = B\)[/tex] or [tex]\(A = -B\)[/tex]. Therefore:
[tex]\[ x - 4 = 11 \][/tex]
or
[tex]\[ x - 4 = -11 \][/tex]
Now solve these two simple equations:
1. For [tex]\(x - 4 = 11\)[/tex]:
[tex]\[ x - 4 = 11 \][/tex]
[tex]\[ x = 11 + 4 \][/tex]
[tex]\[ x = 15 \][/tex]
2. For [tex]\(x - 4 = -11\)[/tex]:
[tex]\[ x - 4 = -11 \][/tex]
[tex]\[ x = -11 + 4 \][/tex]
[tex]\[ x = -7 \][/tex]
So, the solutions are [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex].
Looking at the given choices:
A. [tex]\(x = -15\)[/tex] and [tex]\(x = -7\)[/tex]
B. [tex]\(x = -15\)[/tex] and [tex]\(x = 7\)[/tex]
C. [tex]\(x = 15\)[/tex] and [tex]\(x = -15\)[/tex]
D. [tex]\(x = 15\)[/tex] and [tex]\(x = -7\)[/tex]
The correct answer is:
[tex]\[ \boxed{D. \, x = 15 \text{ and } x = -7} \][/tex]
