Question

Solve for x and graph the solution on the number line below. the number line goes from -12 all the way to 12, please include how I should color the number line, 5x-15≤10, share the Inequality Notation as well

Answer 1

To solve the inequality \(5x - 15 \leq 10\), follow these steps:

### Step 1: Isolate \(x\)
1. Start by adding 15 to both sides:
\[
5x - 15 + 15 \leq 10 + 15
\]
\[
5x \leq 25
\]

2. Next, divide both sides by 5:
\[
\frac{5x}{5} \leq \frac{25}{5}
\]
\[
x \leq 5
\]

### Step 2: Express the solution in inequality notation
The solution can be written as:
\[
x \leq 5
\]

### Step 3: Graph the solution on the number line
1. The solution indicates that \(x\) can take any value up to and including 5.
2. On the number line, you would draw a closed circle (or filled circle) at 5 to indicate that 5 is included in the solution set.
3. Shade the portion of the number line to the left of 5 to represent all numbers less than or equal to 5.

### Number Line Representation
If you visualize the number line from -12 to 12, it will look like this:

```
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
•----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----•=============================
^ |
5 |
```

### Note on Coloring:
- **Coloring the Number Line:** Starting from -12 up to 5 (including 5), shade the area to indicate all values less than or equal to 5. The part of the number line greater than 5 should not be shaded.

### Summary:
- **Inequality Notation:** \(x \leq 5\)
- **Number Line Graph:** Closed circle at 5 with shading to the left of 5.