Posted by JoniAnne on Wednesday, October 20, 2010 at 11:50am.
Please check-
Solve 3 > sqrt(3x)
3x >=o
x>=0/3
x>=0
square both sides and you have 3x < 3^2
3x,9
x<9/3
x<3
answer is 0<=x<3 correct or not?
3(cube) sqrt(2-5) = 3
cube both sides = 2-5x = 27
-5x = 25
x = -5, correct?
Thank you
yes, on the 0=<x=<3
On the
3^3 sqrt (2-5x)=3
Hmmm. I don't know what you meant on the statement.
did you have
cbrt(2-5x)=3 ? if so
2-5x=27
-5x=25
x=-5
Yes, that's what I meant for the second one-thank you for replying
To solve the first inequality, 3 > √(3x), you can follow these steps:
1. Square both sides to eliminate the square root: (3^2) > (√(3x))^2
This simplifies to: 9 > 3x
2. Divide both sides of the inequality by 3 to solve for x:
9/3 > 3x/3
Simplified, this becomes: 3 > x
So, the correct solution is x <= 3.
For the second problem, solving 3^(3) * √(2-5x) = 3:
1. Cube both sides of the equation to eliminate the cube root: (3^(3))^3 * (√(2-5x))^3 = 3^3
Simplifying: 27 * (2-5x)^(3/2) = 27
2. Divide both sides of the equation by 27 to solve for (2-5x)^(3/2):
(2-5x)^(3/2) = 1
3. Cube both sides again to eliminate the square root: [(2-5x)^(3/2)]^2 = 1^2
Simplifying: (2-5x)^3 = 1
4. Solve for (2-5x) by taking the cube root of both sides:
(2-5x) = 1^(1/3)
Simplifying: (2-5x) = 1
5. Solve for x by subtracting 2 from both sides:
-5x = 1-2
Simplifying: -5x = -1
6. Divide both sides by -5 to solve for x:
x = (-1)/(-5)
Simplifying: x = 1/5
So, the correct solution is x = 1/5.