Question

Solver for x and graph the solution on the number line below.

2≤-2x-2≤8

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To solve the inequality for x, we need to manipulate the inequality in such a way that we isolate the variable x. Let's solve the inequality step-by-step:

Given the inequality:
2 ≤ -2x - 2 ≤ 8

First, we'll add 2 to all three parts to cancel out the '-2' alongside the '-2x':
2 + 2 ≤ -2x - 2 + 2 ≤ 8 + 2
4 ≤ -2x ≤ 10

Now, we'll divide throughout by -2 to solve for x. When dividing by a negative value, we need to flip the inequality signs:
4 / -2 ≥ x ≥ 10 / -2
-2 ≥ x ≥ -5

So the solution for x is:
-5 ≤ x ≤ -2

Now let's graph this solution on a number line:

```
-6 -5 -4 -3 -2 -1 0 1
--------------------------
[---|---|---|---|---]
```

In this number line:
- The brackets '[' and ']' represent that -5 and -2 are included in the solution set (because the inequality is "less than or equal to").
- The solid line between -5 and -2 represents all the numbers that are between -5 and -2, including -5 and -2 themselves.