Determine the solution set to the inequality. Express your answer in interval notation.?

Question

-12x + 18 is greater than or equal to -10x + 14

I come up with [2, infinity) but I am not sure enough to settle on it.

Answer 1

-12x + 18 >= -10x + 14

Your first step would be to bring all x terms to the left hand side, and all others to the right hand side. Thus, you get

-12x + 10x >= 14 - 18

Simplify

-2x >= -4

And then divide by -2. ***NOTE*** Whenever you multiply or divide by a negative number, you ALWAYS switch the sign of the inequality. In this case, we'll be switching from >= to <=.

x <= 2

Therefore, the answer is (-infinity, 2]