Solve for xx and graph the solution on the number line below.

To solve the inequality -36 < -5x - 6, we can first add 6 to both sides to isolate the term with x:

-36 + 6 < -5x

-30 < -5x

Next, we divide both sides by -5, remembering to reverse the inequality sign since we are dividing by a negative number:

-30/-5 > x
6 > x

So the first part of the solution is x < 6.

Next, let's solve the inequality -5x - 6 < -46 by adding 6 to both sides:

-5x - 6 + 6 < -46 + 6

-5x < -40

Then, divide both sides by -5, remembering to reverse the inequality sign:

-5x/-5 > -40/-5
x > 8

So the second part of the solution is x > 8.

Combining the two parts, we have x < 6 or x > 8.

Graphing this solution on a number line:

---------------------o---------o---------------------
6 8

The solution is all values of x that are to the left of 6 or to the right of 8, including both of the endpoints.