To solve the inequality [tex]\(4.5x - 100 > 125\)[/tex] and graph the solution on the number line, follow these steps:
1. Isolate the variable [tex]\(x\)[/tex]:
[tex]\[
4.5x - 100 > 125
\][/tex]
Add 100 to both sides of the inequality:
[tex]\[
4.5x - 100 + 100 > 125 + 100
\][/tex]
Simplifying this, we get:
[tex]\[
4.5x > 225
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now, divide both sides by 4.5 to isolate [tex]\(x\)[/tex]:
[tex]\[
x > \frac{225}{4.5}
\][/tex]
Calculating the division gives:
[tex]\[
x > 50
\][/tex]
3. Graph the solution on a number line:
- Draw a horizontal number line.
- Mark the point [tex]\(x = 50\)[/tex] on the number line.
- Use an open circle (or an open dot) at [tex]\(x = 50\)[/tex] because the inequality is strict ([tex]\(>\)[/tex]) and does not include 50 itself.
- Shade or draw an arrow to the right of [tex]\(x = 50\)[/tex] to indicate that [tex]\(x\)[/tex] can take any value greater than 50.
Here's a visual representation:
```
<----|----|----|----|----|----|----|---->
0 10 20 30 40 50 60 70
o----->
```
This graph shows that the solution set includes all real numbers greater than 50, represented by the open circle at 50 and the shaded region (or arrow) extending to the right.
