Question

Which of the following inequalities is true for all real values of x? (Hint: Try plugging in some positive and negative values for x to help see which one works all the time).
Select one:
x^3 ≥ x^2
3x^2 ≥ 2x^3
(2x)^2 ≥ 3x^2
3(x – 2)^2 ≥ 3x^2 – 2

Answer 1

Have you tried to go through and test some values?

Answer 2

idk how

Answer 3

Let's make a table like this. . .

Answer 4

ok

Answer 5

ok

Answer 6

Ok. Now, we are going to test the first possible answer by placing the expression on each side of the inequality into the top of the two empty columns like so . . .

Answer 7

Alright I am writ in this down

Answer 8

Yes, you'll have to test each possible answer to be sure that you have found the correct answer. You can make a chart like this one for each possible answer. Continuing, we can plug in values of x into each expression and calculate corresponding outputs that we place in the two columns like this

Answer 9

ok

Answer 10

What values do you get when you plug in -1 for each expression?

Answer 11

I get -2

Answer 12

-2 isn't the correct value for either expression when x is -1. Recall that. \[x^2 = x * x\] and\[x^3 = x * x * x\] So in this case, when x is equal to -1, x^2 = 1 because -1*-1 = 1

Answer 13

ohhh