To solve the inequality [tex]\(3 - 2x \leq 8\)[/tex]:
1. Isolate the term with [tex]\(x\)[/tex]:
- Start by subtracting 3 from both sides of the inequality to move the constant term to the other side.
[tex]\[
3 - 2x - 3 \leq 8 - 3
\][/tex]
- Simplifying this, you get:
[tex]\[
-2x \leq 5
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
- To isolate [tex]\(x\)[/tex], divide both sides of the inequality by -2. Remember, when you divide or multiply both sides of an inequality by a negative number, you must reverse the direction of the inequality.
[tex]\[
\frac{-2x}{-2} \geq \frac{5}{-2}
\][/tex]
- This simplifies to:
[tex]\[
x \geq -2.5
\][/tex]
3. Represent the answer on a line graph:
- Draw a number line.
- Place a solid dot at [tex]\(x = -2.5\)[/tex] to indicate that [tex]\(x\)[/tex] can be equal to -2.5.
- Shade the region to the right of -2.5 to indicate that [tex]\(x\)[/tex] can be any value greater than -2.5.
The final line graph should look like this:
```
<-------------------|===================>
-2.5
```
Here, the shading to the right of -2.5 indicates [tex]\(x \geq -2.5\)[/tex], meaning [tex]\(x\)[/tex] is greater than or equal to -2.5.
