To determine the value of [tex]\( x \)[/tex] that satisfies the inequality [tex]\( 8x - 6 > 12 + 2x \)[/tex], follow these steps:
1. Isolate the terms involving [tex]\( x \)[/tex] on one side of the inequality:
Start by subtracting [tex]\( 2x \)[/tex] from both sides of the inequality:
[tex]\[
8x - 2x - 6 > 12 + 2x - 2x
\][/tex]
This simplifies to:
[tex]\[
6x - 6 > 12
\][/tex]
2. Isolate the [tex]\( x \)[/tex]-term:
Next, add 6 to both sides of the inequality to further isolate [tex]\( x \)[/tex]:
[tex]\[
6x - 6 + 6 > 12 + 6
\][/tex]
This simplifies to:
[tex]\[
6x > 18
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Finally, divide both sides of the inequality by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{6x}{6} > \frac{18}{6}
\][/tex]
This simplifies to:
[tex]\[
x > 3
\][/tex]
4. Determine which value of [tex]\( x \)[/tex] is in the solution set:
Since the inequality [tex]\( x > 3 \)[/tex] must be satisfied, we need to choose a value greater than 3. The choices provided are:
- [tex]\( -1 \)[/tex]
- [tex]\( 0 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( 5 \)[/tex]
Comparing these values with our solution [tex]\( x > 3 \)[/tex], the value that satisfies this inequality is [tex]\( 5 \)[/tex].
So, the value of [tex]\( x \)[/tex] that is in the solution set is [tex]\( 5 \)[/tex].
