https://file.aiquickdraw.com/mathbot/file/17261545577610gvgby3i.jpg

To solve the inequality \(-2x - 3 > -7\) and identify the correct graph, follow these steps:

### Step 1: Isolate the variable \(x\)
We start by solving for \(x\) step by step.

\[
-2x - 3 > -7
\]

First, add 3 to both sides of the inequality:

\[
-2x > -7 + 3
\]
\[
-2x > -4
\]

### Step 2: Divide by \(-2\)
Since we are dividing by a negative number, the direction of the inequality sign will reverse:

\[
x < \frac{-4}{-2}
\]
\[
x < 2
\]

### Step 3: Interpretation
The solution is \(x < 2\), meaning all values less than 2 are part of the solution set.

### Step 4: Match with the correct graph
The correct graph will have an open circle at \(x = 2\) (because 2 is not included) and an arrow extending to the left, indicating all values less than 2.

Looking at the provided graphs:
- The second graph (from the top) shows an open circle at \(x = 2\) with an arrow extending to the left, representing \(x < 2\).

Thus, **the second graph is the correct representation** of the solution to the inequality \(-2x - 3 > -7\).

---

Do you need further details or have any questions?

### Here are 5 related questions for practice:
1. Solve the inequality \(3x + 4 \leq 7\) and graph the solution.
2. What is the solution to \(4x - 5 > 11\)?
3. How do you solve and graph \(x + 3 \geq 2x - 1\)?
4. Solve and graph the inequality \(-5x + 8 \geq -2x + 4\).
5. Solve for \(x\) in \(2x + 3 < 5x - 6\).

### Tip:
Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number!

Which graph represents the solution to the inequality -2x - 3 > -7?

This lesson explains how to solve the inequality -2x - 3 > -7 step-by-step and how to identify the correct graph. It covers concepts such as inequality manipulation and graph interpretation, suitable for students in Grades 7-9.

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