Sure, let's solve the inequality [tex]\( 0.3(x - 4) > -0.3 \)[/tex] step-by-step and represent the solution on a number line.
1. Step 1: Simplify the inequality
- Start with the given inequality:
[tex]\[
0.3(x - 4) > -0.3
\][/tex]
2. Step 2: Divide both sides by 0.3
- To isolate the term with [tex]\( x \)[/tex], divide both sides of the inequality by 0.3:
[tex]\[
x - 4 > \frac{-0.3}{0.3}
\][/tex]
- Simplify the division on the right-hand side:
[tex]\[
x - 4 > -1
\][/tex]
3. Step 3: Add 4 to both sides
- Add 4 to both sides of the inequality to solve for [tex]\( x \)[/tex]:
[tex]\[
x > -1 + 4
\][/tex]
- Simplify the addition on the right-hand side:
[tex]\[
x > 3
\][/tex]
4. Step 4: Represent the solution on a number line
- The solution to the inequality is [tex]\( x > 3 \)[/tex]. This means that [tex]\( x \)[/tex] can be any value greater than 3 but not equal to 3.
- On the number line, this is represented by an open circle at 3 and a shaded line extending to the right, towards infinity.
Here is what the number line would look like:
```
<---|---|---|---|---|---|---|---|---|--->
0 1 2 3 4 5 6 7 8 9
○=======================>
```
- The open circle at 3 (denoted by ○) indicates that 3 is not included in the solution.
- The arrow extending to the right from the open circle denotes all values greater than 3.
In summary, the solution to the inequality [tex]\( 0.3(x - 4) > -0.3 \)[/tex] is represented on the number line as [tex]\( x > 3 \)[/tex], with an open circle at 3 and a shaded line to the right.
