when you have a greater or less than sign, you can treat it as an equal sign for the purpose of solving an equation. The one thing that you have to remember is that when dividing or multiplying by a negative number, you have to reverse the direction of the < or >
so...
x/(-5) > (-8)
since the x is divided by the -5, you have to multiply both sides by the -5. On the side with the x, it cancels out and you are left with x, on the side with the -8 you get (-8)*(-5) = 40
x < 40 (don't forget, we had to swap the > to a < because we multiplied by the -5)
e^x+3=8 ***subtract 3 from the two facets e^x = 5 ***place "ln" in front of the e and the 5 lne^x = ln5 ***the "lne" equals a million so as that leaves... x = ln 5 answer OR (in basic terms plug Ln5 into the calc to get particular numbers)
Multiply both sides of the inequality by -5 to get
x<40 (the sign of the inequality gets reversed because you are multiplying by a negative number!).
Thus the solutions are all numbers less than 40, or the interval (-infinity,40).