Question

Solver for x and graph the solution on the number line below.
-17<-x-7<-8

Answer 1

To solve for x, we need to isolate it in the inequality -17 < -x - 7 < -8. Here are the steps to do that:

1. Add 7 to all three sides of the inequality:

-17 + 7 < -x - 7 + 7 < -8 + 7
-10 < -x < -1

2. Now, to solve for x, we need to reverse the inequality signs when we multiply or divide by a negative number. In this case, we'll multiply by -1:

-1*(-10) > x > -1*(-1)
10 > x > 1

Alternatively, you can say:

x < 10 and x > 1

Now, let's graph the solution on a number line:

```
1 5 10
Number line: ----|--------|--------|--------|--->
*========*
```

The asterisks (*) and equal signs (=) between 1 and 10 represent the solution set where x is greater than 1 and less than 10. The open circles at 1 and 10 indicate that these endpoints are not included in the solution (since the original inequalities were strictly less than and not less than or equal to).