Answer :
To solve the equation [tex]\(4|x-3|-8=8\)[/tex], we need to handle the absolute value, which requires us to consider two separate cases. Here’s how you can solve it step-by-step:
1. Isolate the absolute value:
[tex]\[
4|x-3| = 16
\][/tex]
We add 8 to both sides to get the absolute value by itself.
2. Divide both sides by 4 to simplify:
[tex]\[
|x-3| = 4
\][/tex]
3. Consider the two cases for the absolute value:
- Case 1: [tex]\(x-3 = 4\)[/tex]
[tex]\[
x = 4 + 3
\][/tex]
[tex]\[
x = 7
\][/tex]
- Case 2: [tex]\(x-3 = -4\)[/tex]
[tex]\[
x = -4 + 3
\][/tex]
[tex]\[
x = -1
\][/tex]
4. Combine the solutions from both cases:
The solutions for the equation are [tex]\(x = 7\)[/tex] and [tex]\(x = -1\)[/tex].
This means the correct solution to the equation is [tex]\(x = -1\)[/tex] or [tex]\(x = 7\)[/tex]. That matches the choice [tex]\(x = -1\)[/tex] or [tex]\(x = 7\)[/tex].
1. Isolate the absolute value:
[tex]\[
4|x-3| = 16
\][/tex]
We add 8 to both sides to get the absolute value by itself.
2. Divide both sides by 4 to simplify:
[tex]\[
|x-3| = 4
\][/tex]
3. Consider the two cases for the absolute value:
- Case 1: [tex]\(x-3 = 4\)[/tex]
[tex]\[
x = 4 + 3
\][/tex]
[tex]\[
x = 7
\][/tex]
- Case 2: [tex]\(x-3 = -4\)[/tex]
[tex]\[
x = -4 + 3
\][/tex]
[tex]\[
x = -1
\][/tex]
4. Combine the solutions from both cases:
The solutions for the equation are [tex]\(x = 7\)[/tex] and [tex]\(x = -1\)[/tex].
This means the correct solution to the equation is [tex]\(x = -1\)[/tex] or [tex]\(x = 7\)[/tex]. That matches the choice [tex]\(x = -1\)[/tex] or [tex]\(x = 7\)[/tex].