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:

try a value of x other than 50 and see if the inequality is satisfied. It is usually convenient to use x=0. Here, that would give 100 -0 ≥ -50, a true statement. So, we now know that solution values are less than or equal to 50: x ≤ 50.Multiply the inequality by -1, or add 3x, so that the coefficient of x is positive. The direction of the comparison symbol for that case will tell you the direction of the comparison symbol in the answer. Here, multiplying by -1 gives -100 +3x ≤ 50, so we know x ≤ 50. If we add 3x instead, we see that 100 ≥ 3x -50, so we know 50 ≥ x.