Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Graph the solution of this inequality: [tex]-2x + 13 \ \textless \ 9[/tex]

Drag a point to the number line.

Sagot :

GinnyAnswer
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].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.