Question

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

5<-x+10 or -x+10≤2

Answer 1

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

Let's solve the two inequalities separately.

First inequality: \(5 < -x + 10\)

Subtract 10 from both sides:
\(5 - 10 < -x\)
\(-5 < -x\)

Now, multiply both sides by -1 and remember to reverse the inequality sign since we are multiplying by a negative number:
\(x < 5\)

Second inequality: \(-x + 10 \leq 2\)

Subtract 10 from both sides:
\(-x \leq 2 - 10\)
\(-x \leq -8\)

Again, multiply both sides by -1 and reverse the inequality sign:
\(x \geq 8\)

So, the solution to the system is where either of the two inequalities is satisfied:

\(x < 5\) or \(x \geq 8\)

This means the solution set consists of all numbers less than 5 combined with all numbers greater than or equal to 8. To graph these solutions on the number line:

1. For the first inequality \(x < 5\), we draw an open circle at 5 and shade to the left of it.
2. For the second inequality \(x \geq 8\), we draw a closed circle at 8 and shade to the right of it.

Here is the number line representation (although it's described in text as I can't create a visual image):

```
...<---|---|---|---|---|---|---|---|---|---|---|---|---|---...
... 3 4 (5) 6 7 [8] 9 10 11 12 13 14 15 ...
```

- Open circle at 5 indicates \(x < 5\) but does not include 5 itself.
- Closed circle at 8 indicates \(x \geq 8\) and includes 8.