https://file.aiquickdraw.com/mathbot/file/172721301223895zh5ksa.jpg

Let's solve the inequality step by step:

The inequality is:

\[
\frac{1 + x}{2} \leq -4
\]

### Step 1: Eliminate the denominator
Multiply both sides of the inequality by 2 to eliminate the denominator:

\[
1 + x \leq -8
\]

### Step 2: Isolate \( x \)
Subtract 1 from both sides to solve for \( x \):

\[
x \leq -9
\]

### Step 3: Interpret the solution
The inequality \( x \leq -9 \) means that the solution set includes all values of \( x \) that are less than or equal to \(-9\).

### Step 4: Analyze the graphs
- The correct graph should have a filled circle at \(-9\) (since \( x \) can equal \(-9\)) and an arrow extending to the left, indicating that the values of \( x \) continue decreasing from \(-9\).

The third graph from the top matches this description: it has a filled circle at \(-9\) and an arrow extending to the left.

Thus, **the third graph** represents the solution to the inequality.

Would you like further details or explanations?

### Related questions:
1. How do you solve inequalities involving fractions?
2. What is the difference between "less than" and "less than or equal to" on a number line?
3. How do you graph inequalities on a number line?
4. What is the process for checking your solution to an inequality?
5. Can inequalities have more than one solution or graph representation?

**Tip:** Always make sure to use filled circles for "less than or equal to" (≤) or "greater than or equal to" (≥), and open circles for strict inequalities (< or >).

Which graph represents the solutions to the inequality (1 + x) / 2 ≤ -4?

Learn how to solve the inequality (1 + x) / 2 ≤ -4 step by step. This guide covers essential algebraic techniques, including multiplying to eliminate denominators and graphing the solution on a number line. Suitable for middle school students in Grades 6-8.

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