Certainly! Let's solve and graph the inequality [tex]\( 0.3(x-4) > -0.3 \)[/tex] on the number line.
### Step-by-Step Solution:
1. Start with the given inequality:
[tex]\[
0.3(x-4) > -0.3
\][/tex]
2. Eliminate the coefficient of [tex]\( (x-4) \)[/tex] by dividing both sides by 0.3:
[tex]\[
\frac{0.3(x-4)}{0.3} > \frac{-0.3}{0.3}
\][/tex]
Simplifying both sides gives:
[tex]\[
x - 4 > -1
\][/tex]
3. Isolate [tex]\( x \)[/tex] by adding 4 to both sides of the inequality:
[tex]\[
x - 4 + 4 > -1 + 4
\][/tex]
Simplifying this, we get:
[tex]\[
x > 3
\][/tex]
### Graphing on the Number Line:
To represent [tex]\( x > 3 \)[/tex] on the number line, follow these steps:
1. Draw a horizontal line and mark a point labeled 3 on it.
2. Since [tex]\( x \)[/tex] must be greater than 3, you’ll draw an open circle at 3 to indicate that 3 is not included in the solution.
3. Draw a ray starting from 3 and extending to the right, indicating all the numbers greater than 3.
Here is the number line representation of the inequality [tex]\( x > 3 \)[/tex]:
```
-∞ | 0 | 1 | 2 | 3 | 4 | 5 | ∞
------------------------------------------------------------------------>
o-------->
3
```
In this graph:
- The open circle at 3 indicates that 3 is not included.
- The arrow pointing to the right indicates that all numbers greater than 3 are included in the solution.
Therefore, [tex]\( x > 3 \)[/tex] is graphically represented on the number line as shown above.
