value of x in solution set

Question

Which value of x is in the solution set of -3x + 8 ≥ 14?

A -3

B -1

C 0

D 3

Answer 1

I used to frequently get stuck on these types of problems back when I was first learning them. The golden rule is whenever you divide by a negative number, the direction of the (<,>,≤,≥) switches. So let's work this one out.

-3x+8≥14

-3x≥6

-x≥2

Now we just need to get rid of the negative (we could have done this in the last step, but I'm breaking it down further for clarity). We do this by dividing both sides by -1, moving the negative to the other side. Since we divided by a negative, the greater than sign has to flip.

x≤-2

Now which value in your solution set is reflected in the choices provided?