Question

Solve for xx and graph the solution on the number line below.
0<x/-5

Answer 1

Your inequality is `0 < x/-5`. To solve for x, you need to isolate x by multiplying both sides of the inequality by -5. When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality flips.

After multiplying both sides by -5, you get:

-5 * 0 < -5 * (x/-5)

This simplifies to:

0 > x

When we multiply by a negative number, we reverse the inequality, so it reads "x is less than 0".

The solution is x < 0, which means that x can be any negative number. On the number line, this would be represented as an arrow pointing to the left from 0, not including 0 itself because the inequality is strict (x is not equal to 0).

Here's a representation of the solution on a number line:

```
Negative infinity <---|----------------0----------------|--- Positive infinity
x
```

In this graph, the "|" mark represents the number 0, and the arrow to the left of 0 shows that all the numbers to the left of 0 are included in the solution set. Note that since it's a strict inequality, there's no closed circle at 0. If it were a closed circle, it would mean that 0 is included in the solution, which it's not in this case.