Question

What is the solution of the equation?

Answer 1

\[4(3-x)^{\frac{ 4 }{ 3 }-5}=59\]

Answer 2

Alright. Do you want to try it on your own first, and see if you can get an answer?

Answer 3

Sure, I'll write it down on paper because solving math on here isn't the easiest.

Answer 4

I agree. You go ahead and try it, if you cannot get it, we will walk through step by step :) No rush

Answer 5

Maybe I will start writing the steps, because I might have to leave and get pizza in a few. xD

Answer 6

What we are going to do is take 4(3-x)^4/3 - 5 = 59 .
Lets add that (-5) to both sides to get;
4(3-x)^4/3 = 64

Answer 7

From here, we will try to remove the "4" so we will have -- > (3-x)^4/3 instead.
So lets divide 4 from each side.
We will then have
(3-x)^4/3 = 16

Answer 8

Now we use the principle of fraction exponents to radicals

Answer 9

A^B/C = c(sqrt(a))^B

Answer 10

\[\sqrt[3]{3-x}^{4} = 16\]

Answer 11

We use the principle of even roots, in this case 4th roots. When taking
even roots we must use ± on the right side. Now since 16 = 2·2·2·2 = 24,
then the 4th root of 16 is 2. So we have:

Answer 12

\[\sqrt[3]{3-x} = \pm 2\]

Answer 13

Next to get rid of the cube root we cube both sides........

Answer 14

(Simply distribute it)

Answer 15

3-x = ± 8

Answer 16

If we use the " + " we get;

3-x = 8
-x = 5
x = -5

Answer 17

If we use the -
we get

3-x = -8
-x = -11
x = 11

Answer 18

Both are valid solutions, when put into the original equation.

Answer 19

Just put them where 'x' is to check, if you are unsure.

Answer 20

Sorry if it was messy or rushed, I had to kind of hurry. xD I wanted to make sure you had the answer in time.

Answer 21

No, that's fine! That makes sense now. Question, when you cubed both sides, why did you drop the exponent of 4?

Answer 22

Because of this...:
We use the principle of even roots, in this case 4th roots. When taking
even roots we must use ± on the right side. Now since 16 = 2·2·2·2 = 24,
then the 4th root of 16 is 2. So we have:\[\sqrt[3]{3-x} = \pm 2\]
By taking the 16 and doing .... 2 x 2 x 2 x 2 = 2^{4} this sort of cancels it out, I guess

Answer 23

Okay, makes sense. Thank you so much! :)):):):):):):)

Answer 24

Not a problem, if you have any more questions, please feel free to tag me!