To determine which value of [tex]\( x \)[/tex] is in the solution set of the inequality [tex]\( 8x - 6 > 12 + 2x \)[/tex], we follow these steps:
1. Move all [tex]\( x \)[/tex] terms to one side of the inequality:
Start with the given inequality:
[tex]\[
8x - 6 > 12 + 2x
\][/tex]
Subtract [tex]\( 2x \)[/tex] from both sides to collect the [tex]\( x \)[/tex]-terms on one side:
[tex]\[
8x - 2x - 6 > 12
\][/tex]
Simplify:
[tex]\[
6x - 6 > 12
\][/tex]
2. Isolate the [tex]\( x \)[/tex]-term:
Add 6 to both sides to remove the constant term on the left:
[tex]\[
6x - 6 + 6 > 12 + 6
\][/tex]
Simplify:
[tex]\[
6x > 18
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides by 6:
[tex]\[
\frac{6x}{6} > \frac{18}{6}
\][/tex]
Simplify:
[tex]\[
x > 3
\][/tex]
4. Determine which provided values of [tex]\( x \)[/tex] satisfy the inequality:
The inequality [tex]\( x > 3 \)[/tex] means [tex]\( x \)[/tex] must be greater than 3. We need to check which of the provided values satisfy this inequality: -1, 0, 3, and 5.
- For [tex]\( x = -1 \)[/tex]: [tex]\(-1\)[/tex] is not greater than 3.
- For [tex]\( x = 0 \)[/tex]: [tex]\(0\)[/tex] is not greater than 3.
- For [tex]\( x = 3 \)[/tex]: [tex]\(3\)[/tex] is not greater than 3; it's equal to 3.
- For [tex]\( x = 5 \)[/tex]: [tex]\(5\)[/tex] is greater than 3.
Therefore, the value of [tex]\( x \)[/tex] that is in the solution set of the inequality [tex]\( 8x - 6 > 12 + 2x \)[/tex] is:
[tex]\[
\boxed{5}
\][/tex]
