Question

Help solving this?

Answer 1

impossible.

Answer 2

Is the answer x=-7/4?

Answer 3

Does x = -7/4 satisfy the equation?

Answer 4

Probably not, I should think — the left side is squared, and the right isn't...tough to make a negative real answer work there!

Answer 5

Okay, Bill, let's think a little harder next time before opening mouth. Yes, -7/4 does satisfy the equation. But it isn't the only solution!

Answer 6

Is x= 5/4 the other?

Answer 7

Yes. Now you should check both solutions in the original equation. You might that one of them doesn't work there, even though it did work in the hint equation...

Answer 8

The original problem was that I didn't know how to solve the equation but I could solve the hint equation so I'm having a little trouble with that.

Answer 9

with x = -7/4
Left hand side:\[(4x+3)^{2/3} = (4(\frac{-7}{4})+3 )^{2/3} = (-4)^{2/3} = (-1)^{2/3}4^{2/3}= 2(-1)^{2/3}\sqrt[3]{2}\]
Right hand side:\[(16x+44)^{1/3} = (16(\frac{-7}{4}) + 44)^{1/3} = 16^{1/3}\]
They aren't equal. That solution is not valid.

with x = 5/4:
Left hand side:\[(4x+3)^{2/3} = (4(\frac{5}{4})+3)^{2/3} = 8^{2/3} = 4\]Right hand side:\[ (16x+44)^{1/3} = (16(\frac{5}{4})+44)^{1/3} = 64^{1/3} = 4\]Those are equal, so that solution is valid.

Answer 10

Thank you!