Diego is solving the inequality 100 − 3x ≥ -50. He solves the equation 100 − 3x = -50 and gets x = 50. What is the solution to the inequality?

  x ≤ 50

Step-by-step explanation:

Since the original inequality includes the "or equal to" case, we know that x=50 is part of the solution set. The trick is to figure out whether the solution set includes values more than 50, or less than 50.

There are a couple of ways to check this:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: