Question

Solve the inequality and graph the solution on the line provided.
3, x, plus, 5, is less than or equal to, 2
3x+5≤
2

Answer 1

To solve the inequality \( 3x + 5 \leq 2 \), follow these steps:

1. **Subtract 5 from both sides**:
\[
3x + 5 - 5 \leq 2 - 5
\]
\[
3x \leq -3
\]

2. **Divide both sides by 3** (since 3 is positive, the direction of the inequality remains the same):
\[
\frac{3x}{3} \leq \frac{-3}{3}
\]
\[
x \leq -1
\]

So, the solution to the inequality is:
\[
x \leq -1
\]

### Graphing the Solution
To graph \( x \leq -1 \) on a number line:

1. Draw a number line.
2. Mark the point \(-1\) on the line.
3. Since the inequality is less than or equal to (\( \leq \)), draw a solid circle at \(-1\) to indicate that \(-1\) is included in the solution.
4. Shade the line to the left of \(-1\) to represent all values less than \(-1\).

The graphical representation would look like this:

```
<------------●========>
-3 -2 -1 0 1 2 3
```

Where \( • \) represents \(-1\), and the shaded area indicates all numbers less than \(-1\) are included in the solution.