Question

Solve for xx and graph the solution on the number line below.
minus, 6, x, is greater than, minus, 12
−6x>
−12

Answer 1

To solve the inequality −6x > −12, we want to isolate x on one side. Dividing both sides of the inequality by −6 will give us x, but remember that when dividing or multiplying an inequality by a negative number, we must flip the inequality sign. So we get:

−6x / (−6) < −12 / (−6)

x < 2

This means that x can be any number less than 2.

Now, to graph the solution on the number line:

1. Draw a number line.
2. Place a point at the number 2.
3. Since x is less than but not equal to 2, we place an open circle at 2 to indicate that it is not included in the solution set.
4. Draw a line extending left from the open circle to indicate all numbers less than 2, and use an arrow to show that it continues indefinitely in that direction.

Here's a representation of what that graph would look like:

```
<---•--------------------
... -3 -2 -1 0 1 2 3 ...
```

Note: The dot (•) at 2 is an open circle, indicating that 2 is not part of the solution. The arrow pointing to the left indicates that all values to the left of 2 are included in the solution set.