Question

For which values of the variable are the following statements true?
Can someone show me how? I want to check my answers when I finish the work.

Answer 1

Well, I'm not sure if this is right, but the first step would probably be to take the 'sqrt' variable, for instance you have:
^3√(x - 5)^3 = x - 5 and √(3x - 1) = 3x - 1
Well, by the square root 'variable' is...
[^3√](x - 5)^3 = x - 5 and [√](3x - 1) = 3x - 1
That means you have '3' and '2', simply multiply it across like the exponents they are, this should give you:
(x - 5)^3 = (x - 5)^3 and (3x - 1) = (3x - 1)^2
So, now divide like you would to get:
x - 5 = x - 5 and 3x - 1 = 3x - 1
In conclusion, we would add the variables together.
2x = 10 and 6x = 2
Now divide.
x = ? and x = ?
I'm not sure if this is the right way to do this or not, but... it's one possible solution.
I already checked the answers, so they're not wrong.
Well, I hope this helps in someway! Have a great day!
{---Ghostgate---}

Answer 2

The answer to these type of questions should be x>=#, x<= # or all real numbers....

Answer 3

For the first, we simplify the exponents, using the multiplication rule (since they are separated by brackets.)

Answer 4

We would do the same for 17, which is also true, since 2 x (1/2)=1!

Answer 5

I would go with alex's answer, he seems like he knows what he's doing.

Answer 6

I guess the threes cancel out and it will also be x-5?