Task 1: abs(7-3x) + 4x > 5

Task 2: sqrt(7-3x) <= x -1

Task 3: sqrt(5-2x) > 1 - x

Task 4: x^2*(1 + 4x^2) < abs(x - 2x^2) + 6 + 4x^3

Printable View

- October 25th 2012, 08:10 AMmiloserdowSolve sevral simple inequalities with modulus and sqrts.
Task 1: abs(7-3x) + 4x > 5

Task 2: sqrt(7-3x) <= x -1

Task 3: sqrt(5-2x) > 1 - x

Task 4: x^2*(1 + 4x^2) < abs(x - 2x^2) + 6 + 4x^3 - October 25th 2012, 09:03 AMHallsofIvyRe: Solve sevral simple inequalities with modulus and sqrts.
If 7- 3x< 0 (that is, if x> 7/3) this is 3x- 7+ 4x> 5. Can you solve that? If so that , this is . Can you solve that?

Quote:

Task 2: sqrt(7-3x) <= x -1

Quote:

]Task 3: sqrt(5-2x) > 1 - x

Quote:

Task 4: x^2*(1 + 4x^2) < abs(x - 2x^2) + 6 + 4x^3

That is, there are two cases:

1) x< 0 or x> 1/2. In this case, so and the inequality becomes which is the same as which is itself the same as . The simplest way to solve that is to find the solutions to and check points between those solutions to see where they are "> 0" and where "< 0".

2) 0< x< 1/2. In this case, so and the inequality becomes which is the same as which is itself the same as . - October 25th 2012, 03:57 PMmiloserdowRe: Solve sevral simple inequalities with modulus and sqrts.
Thank you!