The inequality is:

\[
3X - \frac{5}{4} \leq -1
\]

Let's solve for \(X\):

### Step 1: Add \(\frac{5}{4}\) to both sides.
\[
3X \leq -1 + \frac{5}{4}
\]

Convert \(-1\) to a fraction with the same denominator:
\[
-1 = \frac{-4}{4}
\]

So, the inequality becomes:
\[
3X \leq \frac{-4}{4} + \frac{5}{4}
\]
\[
3X \leq \frac{1}{4}
\]

### Step 2: Divide both sides by 3 to isolate \(X\):
\[
X \leq \frac{1}{4} \div 3
\]
\[
X \leq \frac{1}{12}
\]

### Final answer:
\[
X \leq \frac{1}{12}
\]

Do you want further details or have any questions?

Here are some related questions:
1. How do you solve inequalities with fractions?
2. What happens when you divide both sides of an inequality by a negative number?
3. Can you explain more on converting decimals to fractions?
4. How do you graph the solution to this inequality?
5. How do inequalities differ from equations?

**Tip:** Always check if you need to reverse the inequality when dividing by a negative number.

Learn how to solve the inequality 3X - 5/4 ≤ -1 with a step-by-step solution. This problem covers key algebraic concepts, including working with inequalities and fractions. Suitable for students in Grades 7-8.

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