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.