https://file.aiquickdraw.com/mathbot/file/1726338682725wmckparh.jpg

The inequality shown in the image is:

\[
\frac{7f}{6} \leq \frac{3f + 5}{4}
\]

To solve this inequality:

### Step 1: Eliminate the fractions by multiplying the entire inequality by the least common denominator (LCD) of 6 and 4, which is 12.

\[
12 \cdot \frac{7f}{6} \leq 12 \cdot \frac{3f + 5}{4}
\]

This simplifies to:

\[
2 \cdot 7f \leq 3 \cdot (3f + 5)
\]

\[
14f \leq 9f + 15
\]

### Step 2: Move all the terms involving \(f\) to one side by subtracting \(9f\) from both sides:

\[
14f - 9f \leq 15
\]

\[
5f \leq 15
\]

### Step 3: Solve for \(f\) by dividing both sides by 5:

\[
f \leq 3
\]

### Solution:
The solution is \(f \leq 3\).

Would you like further details or have any questions? Here are some related questions you could explore:

1. How do we solve linear inequalities involving fractions?
2. What is the importance of finding the least common denominator in inequalities?
3. How does multiplying both sides of an inequality affect its direction?
4. What are other methods to solve inequalities with variables on both sides?
5. How can we check the solution of an inequality by substitution?

**Tip:** Always remember to check your solution by substituting it back into the original inequality to verify!

Solve the inequality: (7f/6) ≤ (3f + 5)/4

Learn how to solve the inequality 7f/6 ≤ (3f + 5)/4 using algebraic techniques. This tutorial walks through eliminating fractions, isolating variables, and solving linear inequalities, perfect for students in Grades 8-10.

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