How do I find the correct solution for x?

Question

I'm given this incorrect problem. I need to be able to find the error and correct it...but I'm not sure how to go about doing it

5/x=x-4
x(5/x)=x-4
5=x-4
9=x

????

Answer 1

You can't go from
5/x=x-4
to
x(5/x)=x-4

You should go from
5/x=x-4
to
x(5/x)=x(x-4)

Answer 2

No. x is NOT 9.
You need to do this:
5/x = x-4
Multiply x on both sides to get rid of x at the denominator 5/x.
(x)(5/x) = (x) (x-4)
This gets rid of the x on the LHS because x cancels out:
5 = (x)(x-4)
Then on the RHS, use foil ie. multiply x to each of the term in (x-4). You get:
5 = x^2-4x
^ means superscript. i.e. x to the power of 2. Then you need to get rid of the 5 on the LHS by -5 on both sides
5-5 = x^2 - 4x - 5

0 = x^2 - 4x - 5

Then you have to simplify this expression into factors by finding two same numbers, n1 and n2, that n1 x n2 = -5 and n1 + n2 = -4
It turns out n1 = -5 and n2 = 1.
Substitute n1 = -5x and n2 =1x into 4x like this:
0 = x^2 - 5x + 1x -5
Then factor out the common factor.
0 = x(x -5) + 1(x-5).
Since (x-5) factor is common, you can rewrite the equation like this:
0 = (x-5) (x+1)
Thus x = 5 or x = -1

You can check your answers by using foil for this factor
0 = (x-5) (x+1)
0 = x^2 +x-5x-5
0 = x^2- 4x - 5
You can put this equation back to your original question to show that it is correct.
0 + 5 = x^2 - 4x -5 + 5
5 = x^2 - 4x
5 = x(x-4)
5/x = x-4

I hope this helps.

Answer 3

Whatever you do to one side of an equation, do it also to the other side. Always.
For your problem, you multiplied the left side by x, but you didn't multiply the OTHER SIDE by x. That's the error.
5/x=x-4
x(5/x) = x(x-4)
5=x^2-4x
x^2-4x-5=0
(x-5)(x+1)=0
X=5 or x=-1

Answer 4

on the second step when u multiply (5/x) by x u also have to multiply (x-4) by x so when u multiply (5/x)xthe (x)'s cancle and u have a 5 on one side. when u multiply x by (x-4) u get x^2 aka [x squared] - 4x. so u end up with 5=x^2-4x... from there u subtract the 5 and get x^2-4x-5=0

then u factor into 2 binomials and get (x-5)and(x+1)

u set both of them to zero x-5=0 & x+1=0

x=(5) & x=(-1)

Answer 5

x = -1 & x = 5

Okay we have 5/x = x-4.
Multiply both sides by x, to get 5x/x = x(x-4).
Then, 5 = x^2 - 4x
Then, x^2 - 4x - 5 = 0
Factor: x^2 - 4x - 5 = 0 is the same as (x + 1)(x - 5) = 0

Or, use the quadratic formula to solve for x.

So x = -1 & x = 5

Answer 6

the problem i in the second part of the problem they didn't forget to multiply the x on the other side of the problem
it should be
x(5/x)=x(x-4)
5=x^2-4x
x^2-4x-5=0
(x-5)(x+1)
x=5,-1

Answer 7

multiply by x on both sides instead

u get 5 = x 2nd - 4x

x2nd -4x -5= 0

Answer 8

no Im pretty sure you do this, and if you put a 1 infront of the x it will help you and you can check your answere...
5/1x =x-4
1x(5)= x-4 x+4
5= 4x
5/5= 4x/5
x = .8
5/.8 = .8-4
I hope thats right cause i havent done any math all summer!!!

Answer 9

the goal is to get numbers on one side and the variables(x) on the other. You do this by doing the same thing on both sides. The error here is that they multiplied the left side by x but didn't do the same on the right side.

Answer 10

x(5/x)=x(x-4)
5=x(x-4)
0=x(squared)-4x-5
0=(x-5)(x+1)
x=5 or -1

from an old math teacher:):):)

Answer 11

mistake is in the second step, hint, you multiply the same thing to keep both the side of the equation equal.