SOLUTION: Which of the following inequalities is true for all real numbers? x^3 > or equal to x^2 3x^2 > or equal to 2x^3 (2x)^2 > or equal to 3x^2 3(x-2)^2 > or equal to 3x^2 - 2

Algebra ->  Inequalities -> SOLUTION: Which of the following inequalities is true for all real numbers? x^3 > or equal to x^2 3x^2 > or equal to 2x^3 (2x)^2 > or equal to 3x^2 3(x-2)^2 > or equal to 3x^2 - 2      Log On


   

Question 737197: Which of the following inequalities is true for all real numbers?
x^3 > or equal to x^2
3x^2 > or equal to 2x^3
(2x)^2 > or equal to 3x^2
3(x-2)^2 > or equal to 3x^2 - 2
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify/solve each one using algebra.


x%5E3+%3E=+x%5E2 Divide both sides by x%5E2


x%3E=+1 That's only true for real numbers 1 or greater.


3x%5E2+%3E=+2x%5E3 Divide both sides by x%5E2 and divide both sides by 2.


3%2F2+%3E=+x Only true for real numbers less than or equal to 3/2.


%282x%29%5E2+%3E=+3x%5E2


4x%5E2+%3E=+3x%5E2 Divide both sides by x%5E2


4+%3E=+3 That's always true.


3%28x-2%29%5E2+%3E=+3x%5E2+-+2


3x%5E2+-+12x+%2B12+%3E=+3x%5E2+-+2


-12x+%3E=+-14


x%3E=+7%2F6 Not true for all real numbers.

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)