How to solve this inequality

1) -3x^3 >= 81

and which of the following inequalities has a solution

2) x-3<3-x<x-5 or x-3>3-x>x-5

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- Oct 4th 2013, 06:08 AMdarkangel06Inequalities
How to solve this inequality

1) -3x^3 >= 81

and which of the following inequalities has a solution

2) x-3<3-x<x-5 or x-3>3-x>x-5 - Oct 4th 2013, 06:24 AMPlatoRe: Inequalities
- Oct 4th 2013, 06:35 AMHallsofIvyRe: Inequalities
What Plato said! And the fact that $\displaystyle x^3$ is an increasing function.

Quote:

and which of the following inequalities has a solution

2) x-3<3-x<x-5 or x-3>3-x>x-5

x- 3> x- 5 is the same as -3> -5 which is true. - Oct 4th 2013, 06:38 AMvotanRe: Inequalities
- Oct 4th 2013, 06:42 AMdarkangel06Re: Inequalities
for the second one It just says to explain which one equality has a solution.

and in the answers the second inequality has a solution but i really dont know how :/ - Oct 4th 2013, 06:56 AMvotanRe: Inequalities
first: x - 3 < 3 - x < x - 5

x < 3 OR x > 4 (OR condition if the double inequality were two separate inequalties) no AND solution

*******3......4******** (* means solultion)

second: x - 3 > 3 - x > x - 5

x > 3 AND x < 4 (AND condition)

.........3*******4......... - Oct 4th 2013, 07:04 AMdarkangel06Re: Inequalities
Ok so how did you get x>3 and x< 4 in the second equation

- Oct 4th 2013, 10:11 AMvotanRe: Inequalities
x - 3 > 3 - x > x - 5

Split this into two inequalities:

x - 3 > 3 - x ==> x + x > 3 + 3 ==> 2x > 6 ==> x > 6/2 = 3 (group all x's on one side and the numbers on the other side)

3 - x > x - 5 == 3 + 5 > x + x ==> 8 > 2x ==> (8/2) > x or x < 4 by reading the inequality from right to left.