Question

Solve and graph this inequality: 3-x/2 ≤2

Answer 1

To solve the inequality \( 3 - \frac{x}{2} \leq 2 \), we can follow these steps:

1. **Isolate the term involving \( x \)**:

Subtract 3 from both sides:

\[
3 - \frac{x}{2} - 3 \leq 2 - 3
\]

This simplifies to:

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

2. **Eliminate the negative sign**:

We can multiply both sides by -1, but remember to reverse the inequality sign:

\[
\frac{x}{2} \geq 1
\]

3. **Solve for \( x \)**:

Multiply both sides by 2:

\[
x \geq 2
\]

So the solution to the inequality is \( x \geq 2 \).

### Graphing the Inequality

To graph this inequality on a number line:

1. Draw a number line.
2. Mark the point \( 2 \) on the number line.
3. Since the inequality is \( x \geq 2 \), we will use a closed circle at 2 to indicate that 2 is included in the solution.
4. Shade the line to the right of 2 to show all numbers greater than 2.

Here is a simple representation of the number line:

```
---|---|---|---|---|---|---|---|---|---|---
... 0 1 2 3 4 5 6 7 8 9 ...
●========================>
```

The filled circle at \( 2 \) represents that \( 2 \) is included in the solution, and the shaded area to the right indicates all numbers greater than \( 2 \).