To solve the inequality [tex]\(-2x + 13 < 9\)[/tex], we follow these steps:
1. Isolate the variable [tex]\(x\)[/tex]:
[tex]\[
-2x + 13 < 9
\][/tex]
2. Subtract 13 from both sides to begin isolating [tex]\(x\)[/tex]:
[tex]\[
-2x + 13 - 13 < 9 - 13
\][/tex]
[tex]\[
-2x < -4
\][/tex]
3. Divide both sides by [tex]\(-2\)[/tex]. Since we're dividing by a negative number, we need to reverse the inequality sign:
[tex]\[
x > 2
\][/tex]
So, the solution to the inequality [tex]\(-2x + 13 < 9\)[/tex] is [tex]\(x > 2\)[/tex].
To graph the solution [tex]\(x > 2\)[/tex] on a number line:
- Place an open circle at [tex]\(2\)[/tex] to indicate that [tex]\(2\)[/tex] is not included in the solution set.
- Shade the number line to the right of [tex]\(2\)[/tex] to represent all numbers greater than [tex]\(2\)[/tex].
Here's how this should look:
```
-5 -4 -3 -2 -1 0 1 2 3 4 5
o-------->
```
- The open circle at [tex]\(2\)[/tex] signifies that [tex]\(x > 2\)[/tex].
- The arrow extending rightward shows that the solution includes all numbers greater than [tex]\(2\)[/tex].
