To solve the compound inequality [tex]\(8 > 3x - 1 > 5\)[/tex], we need to break it down into two separate inequalities and solve each one individually.
1. First Inequality: [tex]\(8 > 3x - 1\)[/tex]
- Start with the inequality:
[tex]\[
8 > 3x - 1
\][/tex]
- Add 1 to both sides of the inequality to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
8 + 1 > 3x \implies 9 > 3x
\][/tex]
- Divide both sides by 3:
[tex]\[
\frac{9}{3} > x \implies 3 > x
\][/tex]
2. Second Inequality: [tex]\(3x - 1 > 5\)[/tex]
- Start with the inequality:
[tex]\[
3x - 1 > 5
\][/tex]
- Add 1 to both sides of the inequality to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
3x - 1 + 1 > 5 + 1 \implies 3x > 6
\][/tex]
- Divide both sides by 3:
[tex]\[
\frac{3x}{3} > \frac{6}{3} \implies x > 2
\][/tex]
Now, combine the results of the two inequalities. We have:
[tex]\[
3 > x \quad \text{and} \quad x > 2
\][/tex]
This can be written as:
[tex]\[
3 > x > 2
\][/tex]
Among the given options, the correct selection is:
c. [tex]\(3 > x > 2\)[/tex]
