SOLUTION: If k = (x + 3)/(x - 4) and k^2 - 3k = 28, find x. I say replace every k with (x + 3)/(x - 4). I get this: [(x + 3)/(x - 4)]^2 - 3[(x + 3)/(x - 4)] = 28 Correct

Algebra.Com
Question 1207662: If k = (x + 3)/(x - 4) and k^2 - 3k = 28, find x.

I say replace every k with (x + 3)/(x - 4).

I get this:

[(x + 3)/(x - 4)]^2 - 3[(x + 3)/(x - 4)] = 28

Correct?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
that looks reasonable, although it might get messy.

you can also do the following:

in the equation k^2 - 3k = 28, subtract 28 from both sides to get:
k^2 - 3k - 28 = 0
factor this quadratic equation to get:
(k-7) * (k+4) = 0
solve for k to get:
k = 7 or k = -4

in the equation k = (x + 3)/(x - 4), replace k with 7 and solve for x.
after you do that, replace k with - 4 and solve for x.

you should get x = 31/6 or x = 13/5.

it should be able to be solved the way that you showed, but i think solving for k first is probably easier.


Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
If k = (x + 3)/(x - 4) and k^2 - 3k = 28, find x.
~~~~~~~~~~~~~~~~~~~~~ 

First solve the quadratic equation for k and find its solutions for k.


    k^2 - 3k = 28

is equivalent to

    k^2 - 3k - 28 = 0.


Factor left side

    (k-7)*(k+4) = 0.


The solutions are k= 7 and k= -4.


        Now consider and solve equation   = k   
        for two values of k: k= 7 and  k= -4.



(a)  Case k = 7.

     Now solve equation

           = 7

     Step by step

          x+3 = 7*(x-4)

          x+3 = 7x - 28

           3 + 28 = 7x - x

            31 = 6x

             x = .



(b)  Case k = -4.

     Now solve equation

           = -4

     Step by step

          x+3 = (-4)*(x-4)

          x+3 = -4x + 16

           x + 4x = 16 - 3

            5x = 13

             x = .


ANSWER.  Two solutions are  x =   and  x = .

Solved from the beginning to the end, with complete explanations.



RELATED QUESTIONS

If k = (x + 3)/(x - 4) and k^2 - 3k = 28, find k. (answered by Edwin McCravy)
28 x .0250+K ___________ =.0250... (answered by edjones)
Match the corresponding function formula with each function when h(x) = 3x + 2 and g(x) = (answered by stanbon)
find k such that for every real x we have (1 + kx)/(1 + x^2) < k The answer is k... (answered by tommyt3rd)
Find the values of k if 3(x+3)^4 - (k+x)^2 has a factor... (answered by KMST)
f(x) = x^3 + (1 - k^2)x + k (a) Show that -k is a root of f. I've already solved this (answered by jsmallt9)
if (x-2)(x+3)=k, what is... (answered by reviewermath,josgarithmetic)
if x^6+kx^5+x^4+kx^3+3x^2-k+2 is a multiple of (x-k) find the value of... (answered by jsmallt9)
For what value of 'k' the equation {{{ x^2 + k(2x+3) + 4(x+2) + 3k-5}}} is a perfect... (answered by josgarithmetic)