Question

Solve for xx and graph the solution on the number line below.
1, is greater than or equal to, start fraction, x, divided by, 3, end fraction
1≥
3
x
​
the number line goes from-12 to 12, answer how I would shade that

Answer 1

To solve the inequality \( 1 \geq \frac{x}{3} \), we can follow these steps:

1. **Multiply both sides by 3**: Since we are multiplying by a positive number, the direction of the inequality remains the same.
\[
3 \cdot 1 \geq 3 \cdot \frac{x}{3}
\]
\[
3 \geq x
\]
This can also be written as:
\[
x \leq 3
\]

2. **Determine the solution set**: The solution to the inequality \( x \leq 3 \) means that \( x \) can take any value less than or equal to 3.

3. **Graph the solution on the number line**:
- Mark the number 3 on the number line.
- Since \( x \) is less than or equal to 3, you will shade all the numbers to the left of 3, including 3 itself (usually denoted with a closed dot at 3 to show that it is included).

Here’s how you would visualize it on the number line from -12 to 12:

```
-12 -10 -8 -6 -4 -2 0 2 3 4 6 8 10 12
|---------|--------|--------|--------|--------|-------|-------|-------|-------|-------|-------|-------|
<--------- (closed dot at 3)=========================>
```

The arrow on the left signifies that the shading goes indefinitely in the negative direction (to the left of 3). The closed dot at 3 indicates that 3 is part of the solution set.