Solve for xx and graph the solution on the number line below.

Question

x-8<-10 or x-8≥-2

Answer 1

To solve for x in each part of the compound inequality, we'll solve each inequality separately.

For the first inequality:

x - 8 < -10

We add 8 to both sides to isolate x:

x < -10 + 8
x < -2

For the second inequality:

x - 8 ≥ -2

We add 8 to both sides:

x ≥ -2 + 8
x ≥ 6

Now, we combine the solutions:

x < -2 or x ≥ 6

This means that x can be any number less than -2 or any number greater than or equal to 6.

To graph this on a number line, we will use:

- An open circle at -2 to signify that -2 is not included in the solution set (since the inequality is strictly less than -2).
- A closed circle at 6 to indicate that 6 is included in the solution set (since the inequality is greater than or equal to 6).
- A line extending to the left from -2 indicating all the numbers less than -2.
- A line extending to the right from 6 indicating all the numbers greater than or equal to 6.

Please note that I cannot draw a graph on this platform, but here's a description of what it would look like:

```
Number line: ----<----(-2)---->----[6]---->----
```

In the number line:

- "----<----" part indicates that the values continue indefinitely to the left beyond -2.
- "(-2)" represents the open circle at the point -2.
- "---->----" part between -2 and 6 indicates that the values between -2 and 6 are not part of the solution set.
- "[6]" represents the closed circle at the point 6.
- "---->----" part to the right of 6 indicates that the values continue indefinitely to the right from 6.

This number line represents the solution to the inequality x < -2 or x ≥ 6.