https://file.aiquickdraw.com/mathbot/file/1728232035960yc7afub0.jpg

Let's break down the inequality presented in the image:

The inequality is: 
\[
\frac{1}{2}x + 4 \leq 1
\]

### Step 1: Isolate the variable term

We want to move the constant (4) to the other side. To do this, subtract 4 from both sides:
\[
\frac{1}{2}x + 4 - 4 \leq 1 - 4
\]
\[
\frac{1}{2}x \leq -3
\]

### Step 2: Eliminate the fraction

Now, to eliminate the fraction \(\frac{1}{2}\), multiply both sides by 2:
\[
2 \times \frac{1}{2}x \leq 2 \times (-3)
\]
\[
x \leq -6
\]

### Final Inequality:
The solution is:
\[
x \leq -6
\]

### Graphing the Solution:
- Since the inequality is \(x \leq -6\), we use a closed circle at \(-6\) and shade to the left, indicating all values less than or equal to \(-6\).

Looking at the choices in the image, **Option A** matches this solution. It shows a closed circle at \(-6\) and shading to the left.

Would you like further details, or do you have any questions?

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Here are 5 related questions to deepen your understanding:
1. How would the solution change if the inequality were \(x + 4 \leq 1\) instead?
2. What would the graph look like if the inequality were strict, i.e., \(\frac{1}{2}x + 4 < 1\)?
3. How would the graph change if the inequality were \(x \geq -6\) instead of \(x \leq -6\)?
4. Can you solve \(\frac{3}{4}x + 5 \leq 2\) using the same steps?
5. How would multiplying or dividing by a negative number affect the inequality?

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

Solve the inequality: (1/2)x + 4 ≤ 1 and graph the solution.

Learn how to solve and graph the inequality (1/2)x + 4 ≤ 1. The solution involves algebraic manipulation and graphing techniques, including shifting constants and multiplying both sides of the inequality.

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