Please check-
Solve 3 > sqrt(3x)
3x >=o
x>=o/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
1. Correct.
2. 3^3*sqrt(2 - 5x) = 3,
27*sqrt(2 - 5x) = 3,
Divide both sides by 27:
sqrt(2 - 5x) = 3/27 = 1/9,
Square both sides and get:
2 - 5x = 1/81,
-5x = 1/81 - 2,
-5x = 1/81 - 162/81,
-5x = -161/81,
Multiply both sides by -1/5:
x = (-161 / 81) * (-1/5) = 161 / 405.
CHECK:
3^3*sqrt(2 - (5*161/405)) =
27*sqrt(2 - 1.9877) =
27*sqrt(0.01235) =
27 * 0.11111 = 3.
Let's go through each of the equations and steps you provided one by one.
1. Solve 3 > sqrt(3x):
To solve this inequality, we need to isolate the variable x. We begin by squaring both sides of the inequality to eliminate the square root:
(3)^2 > (sqrt(3x))^2
9 > 3x
Now, divide both sides of the inequality by 3 to solve for x:
9/3 > 3x/3
3 > x
The solution to the inequality is x < 3.
2. Solve 3(cube) sqrt(2-5) = 3:
It appears there might be a typing mistake in this equation. If the equation is 3^(3√(2-5)) = 3, then we can solve it as follows:
First, cube both sides of the equation to eliminate the cube root:
(3^(3√(2-5)))^3 = 3^3
2-5 = 27
-3 = 27
This leads to a contradiction because -3 is not equal to 27. Therefore, there is no solution to this equation.
Regarding your question about the answer x = -5, let's confirm it:
You mentioned "cube both sides = 2 - 5x = 27," but it seems there might be a mistake since the right-hand side should be the cube of something. Could you please provide the correct equation or clarify your question?
Feel free to provide more information or ask additional questions.