https://file.aiquickdraw.com/mathbot/file/1727217468668sad3ry34.jpg

Let's solve the inequality step by step.

The inequality is:

\[
17 \leq -2m - 3
\]

### Step 1: Isolate the variable term (-2m)
To isolate the variable term, we first add 3 to both sides of the inequality:

\[
17 + 3 \leq -2m
\]

\[
20 \leq -2m
\]

### Step 2: Solve for \(m\)
Next, divide both sides of the inequality by \(-2\). **Remember**, when dividing or multiplying both sides of an inequality by a negative number, the inequality symbol must flip.

\[
\frac{20}{-2} \geq m
\]

\[
-10 \geq m \quad \text{or} \quad m \leq -10
\]

### Final Answer:
The solution is:

\[
m \leq -10
\]

This inequality means that \(m\) must be less than or equal to \(-10\).

Would you like further details on any part of this solution, or do you have any questions?

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Here are five related questions you might explore:
1. How does the inequality change if you divide both sides by a positive number?
2. What happens if the inequality had been \(17 \geq -2m - 3\)?
3. How would you solve a similar inequality involving fractions?
4. How can you graph the solution \(m \leq -10\) on a number line?
5. Can you solve \(17 \leq -2m - 3\) if the coefficients are decimals instead of integers?

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

Learn how to solve the inequality 17 ≤ -2m - 3 using algebraic steps. This guide covers isolating the variable and handling inequalities, including reversing the inequality sign when dividing by a negative number. Suitable for Grades 7-9 students.

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