To solve the inequality [tex]\(\frac{3}{8} x > 9\)[/tex], follow these steps:
1. Write down the inequality:
[tex]\[
\frac{3}{8} x > 9
\][/tex]
2. Isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], you need to eliminate the fraction [tex]\(\frac{3}{8}\)[/tex] that is multiplied by [tex]\(x\)[/tex]. You can do this by multiplying both sides of the inequality by the reciprocal of [tex]\(\frac{3}{8}\)[/tex], which is [tex]\(\frac{8}{3}\)[/tex].
3. Multiply both sides by [tex]\(\frac{8}{3}\)[/tex]:
[tex]\[
\left(\frac{8}{3}\right) \cdot \frac{3}{8} x > 9 \cdot \left(\frac{8}{3}\right)
\][/tex]
4. Simplify the left side:
The [tex]\(\frac{8}{3}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex] will cancel each other out, leaving:
[tex]\[
x > 9 \cdot \left(\frac{8}{3}\right)
\][/tex]
5. Calculate the right side:
[tex]\[
x > 9 \cdot \frac{8}{3} = 9 \cdot \frac{8}{3} = 3 \cdot 8 = 24
\][/tex]
The inequality simplifies to:
[tex]\[
x > 24
\][/tex]
Therefore, the solution of the inequality [tex]\(\frac{3}{8} x > 9\)[/tex] is:
C. [tex]\(x > 24\)[/tex]
