When I asked you about the following problem:Solve 4sqrt(6x-2)>4
The first 4 is outside the square root sign and then (6x-2) is under the square root sign >4. You said to do the following. Divide by 4 to get
sqrt(6x-2)>1
For this to happen, 6x-2>1 or x>(1/2)
which does not match any of your answers.
I suspect there is a misprint or misinterpretation of the question.
Wouldn't I say (4sqrt(6x-2))^4 > 4^4 because I take
6x-2 > 256
6x>258
x >43
and 6x-2>=0
6x-2>=2
x>=1/3
but when I put 1/3 back in, I don't think it works, does it so that's why I said x>43 and not the other answers available which would be
1/3<=x<43
1/3<x<43
x>=1/3
x>43
Could someone please recheck the solution to the above problem-Mathmate said it can't be done but I think it was just interpreted the wrong way-please recheck m solution
Thank you
If the expression was the fourth root, it would be more understandable to write it as:
(6x-2)^(1/4) > 4
in which case x>43 is the correct answer.
Alternatively, you could add a note to say that the left-hand-side is the fourth root.
Thank you
I apologize for any confusion caused by my previous response. Let's reevaluate the problem to find the correct solution.
The original inequality is 4√(6x-2) > 4.
To solve this inequality, we need to isolate the variable x. Here's how we can approach it:
1. Divide both sides of the inequality by 4:
(4√(6x-2))/4 > 4/4
√(6x-2) > 1
2. Now, to square both sides of the inequality to eliminate the square root:
(√(6x-2))^2 > (1)^2
6x - 2 > 1
3. Add 2 to both sides of the inequality:
6x - 2 + 2 > 1 + 2
6x > 3
4. Divide both sides of the inequality by 6:
(6x)/6 > 3/6
x > 1/2
Therefore, the correct solution to the inequality 4√(6x-2) > 4 is x > 1/2.
It seems there might have been a misunderstanding in your interpretation of the original inequality. The given inequality asks for values of x that make the expression 4√(6x-2) greater than 4, not squared. Thus, the solution is x > 1/2, and your suggestion of x > 43 does not match the problem context.