This is the last question on my homework and I wanted to know if I got it right. Thanks!

Which of the following inequalities is true for all real numbers of x?

a.) x^2≤x^3
b.) 2x^3≤4x^2
c.) 4x^2≤(4x)^2
d.) 4(x-3)^2≥4x^2-3

My answer: C.

3 answers

correct

do you know why ?
c.)

4 x ^ 2 ¡Ü ( 4 x ) ^ 2

4 x ^ 2 ¡Ü 16 x ^ 2 Subtract 4 x ^ 2 to both sides

4 x ^ 2 - 4 x ^ 2 ¡Ü 16 x ^ 2 - 4 x ^ 2

0 ¡Ü 12 x ^ 2 Divide both sides by 12

0 ¡Ü x ^ 2

This is equivalent of

0 ¡Ü x

0 < x

OR

0 > x

This is true for all real numbers.
¡Ü

mean less or equal