Solve for a and graph the solution.
–
1≥
–
3a–2/2
>–
7
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

Let's solve for \( a \) in the given inequality:

\[
1 \geq \frac{-3a - 2}{2} > -7
\]

### **Step 1: Break into Two Inequalities**
Since this is a compound inequality, we solve it in two parts:

1. **Solve** \( 1 \geq \frac{-3a - 2}{2} \):

\[
1 \times 2 \geq -3a - 2
\]

\[
2 \geq -3a - 2
\]

\[
2 + 2 \geq -3a
\]

\[
4 \geq -3a
\]

\[
\frac{4}{-3} \leq a
\]

\[
a \geq -\frac{4}{3}
\]

2. **Solve** \( \frac{-3a - 2}{2} > -7 \):

\[
\frac{-3a - 2}{2} \times 2 > -7 \times 2
\]

\[
-3a - 2 > -14
\]

\[
-3a > -12
\]

\[
a < 4
\]

### **Step 2: Write the Solution**
The solution is:

\[
-\frac{4}{3} \leq a < 4
\]

### **Step 3: Graph the Solution**
- The left endpoint is at \( -\frac{4}{3} \) and is **closed** because of \( \leq \).
- The right endpoint is at \( 4 \) and is **open** because of \( < \).
- The solution is the interval \( \left[ -\frac{4}{3}, 4 \right) \).

Would you like a graph for better visualization?

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### **Related Questions**
1. How do you graph compound inequalities on a number line?
2. What is the difference between an open and closed interval?
3. How do you solve absolute value inequalities?
4. How do you convert an inequality to interval notation?
5. How does multiplying by a negative number affect inequality signs?

### **Math Tip:**  
When multiplying or dividing by a negative number in an inequality, **always** flip the inequality sign!

Solve for a and graph the solution. 1 ≥ (-3a - 2)/2 > -7. Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

Learn how to solve the compound inequality 1 ≥ (-3a - 2)/2 > -7 and graph the solution on a number line. This step-by-step explanation covers solving inequalities, applying the multiplication property of inequalities, and representing the solution in interval notation. Suitable for students in Grades 8-10.

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