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We are given the inequality:

\[
4x - 5y \leq -3
\]

The task is to substitute \( x = -3 \) and solve for \( y \). Let's proceed with that.

### Step 1: Substitute \( x = -3 \) into the inequality

\[
4(-3) - 5y \leq -3
\]

\[
-12 - 5y \leq -3
\]

### Step 2: Add 12 to both sides

\[
-5y \leq -3 + 12
\]

\[
-5y \leq 9
\]

### Step 3: Divide both sides by -5

Since we are dividing by a negative number, we need to reverse the inequality sign.

\[
y \geq \frac{9}{-5}
\]

\[
y \geq -\frac{9}{5}
\]

Thus, the solution is \( y \geq -\frac{9}{5} \), which corresponds to **option C**.

---

Would you like further details or have any questions about the steps? Here are 5 related questions:

1. How do we solve inequalities when dividing by a negative number?
2. Why did the inequality sign flip during the division step?
3. How can we check the solution to an inequality problem?
4. What happens when you substitute different values for \( x \)?
5. What if we had been asked to solve an equality instead of an inequality?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing by a negative number.

For this two-variable inequality, put the number -3 in for x and find the set of matching numbers for y. Solve 4x - 5y ≤ -3 when x = -3.

Learn how to solve the two-variable inequality 4x - 5y ≤ -3 by substituting x = -3. This step-by-step solution shows how to solve for y while applying inequality properties. Suitable for students in Grades 7-9.

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