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:

100-3x≥-50

subtracting 100 at both side on inequality

-100+100-3x≥--50-100

-3x≥-150

Dividing both sides by 3

-3x/3≥-150/3

-x≥--50

Adding 50 on both sides

-x+50≥-50+50

-x+50≥0

Adding x on both sides

-x+x+50≥0+x

50≥x

so,

x≤50

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.