Let's solve the inequality [tex]\(\frac{1}{3} s - 6 < 24\)[/tex] step-by-step.
### Step-by-Step Solution:
1. Start with the given inequality:
[tex]\[
\frac{1}{3} s - 6 < 24
\][/tex]
2. Isolate the term with [tex]\(s\)[/tex] on one side. To do this, we'll first add 6 to both sides of the inequality:
[tex]\[
\frac{1}{3} s - 6 + 6 < 24 + 6
\][/tex]
Simplify:
[tex]\[
\frac{1}{3} s < 30
\][/tex]
3. Eliminate the fraction by multiplying both sides of the inequality by 3, which is the coefficient of [tex]\(s\)[/tex]:
[tex]\[
3 \cdot \frac{1}{3} s < 30 \cdot 3
\][/tex]
Simplify:
[tex]\[
s < 90
\][/tex]
4. Write the final solution set.
The solution set of the inequality is:
[tex]\[
\{ s \mid s < 90 \}
\][/tex]
### Conclusion:
The correct solution from the given options is:
[tex]\[
\{ s \mid s < 90 \}
\][/tex]
