How do you solve 4/x+3=6/4-x ?

Question

Please tell me what to do step by step

but how do you get x=-1.5

Answer 1

cross-multiply : 4/x+3 = 6/4-x is the same as 4(4-x)=6(x+3), so 16-4x = 6x +18 :
16-18 = 6x + 4x
-2 = 10x
-2/10 = 10x/10
-0.2=x ( which is the same as x = -1/5 not -1.5)

Answer 2

As it has already been pointed out, without a clearly defined equation it is pointless trying to give you an answer.

Mathematical problems posed in these pages suffer from the limitations of mathematical symbols which may or may not be available.

Accepting 4/x means 4 divided by x, then:

4/x + 3 = 6/4 - x This is a Quadratic Equation and the Equation now becomes:

X (squared) + 3/2X + 4 = 0

This is where the term 3/2 i.e. 1.5 comes from

The value for X using a standard formula results in the square root of a negative (-) quantity i.e. an unreal root/s and there is no solution.

The standard formula for the solution of a quadratic equation appears in any mathematical text book which includes algebra,

Alternatively search Google for 'Quadratic Equation'

There can be no other solution since no brackets appear within the equation.

Answer 3

The question is ambiguous. When you type an equation on Homework Help etc. you cannot arrange symbols and punctuation as you would with pencil and paper, so place brackets to make your meaning clear. If I guessed wrong then, as Sherlock Holmes would've said, you know my methods: apply them.

I divine that you mean

4 / (x + 3) = 6 / (4 - x)

Multiply both sides by (x + 3)(4 - x)

4(4 - x) = 6(x+3)

16 - 4x = 6x + 18

-10x = 2

*** x = -1/5 (negative one fifth or -0.2) *** Answer

Check:
Substitute x = (-0.2) in the original equation
4 / ((-0.2) + 3) = 6/(4 - (-0.2)) is identical to
4 / 2.8 = 6 / 4.2 (subtracting negative 0.2)
40/28 = 60/42 Bring to a common denominator of 7
10/7 = 10/7 Correct

Answer 4

Hi,

it's important to be sure what your original equation is. Is it:

4/(x + 3) = 6/(4 - x) - Equation (1)

or:

(4/x) + 3 = (6/4) - x - Equation (2)

Each require a different method, and give a different answer. I imagine it is Equation (1), in which case JDN's answer is correct. Equation (2) is more difficult, as shown by Ash. This gives a quadratic equation without a solution in the real domain. There is still a solution in something called the imaginary domain - something to look forward too!

Answer 5

Note: x.x is xsquared

4/x + 3 = 6/4 - x

Multiplying by 4x on both sides,

16 + 12x = 6x - 4x.x

Bringing all terms on LHS,

4x.x - 6x + 12x + 16 = 0

4xx +6x +16 = 0

Dividing by 2 on both sides,

2xx + 3x + 8 = 0

.....???

I guess the sum is wrong/// Sorry...

Answer 6

4/x + 3 = 6/4 - x
4/x + x = 6/4-3
(4+x sq.) /x = 6-12/4
4+x sq. = -6x/4
16+4x sq.= -6x
4 x sq. +6x -16=0
2 x sq. +3x -8 =0
Solve like any other quadratic equation

Answer 7

cross multiply
4(4-x) = 6(x+3)
16-4x = 6x+18
16-18 = 6x+4x
-2 = 10x
x = -2/10
x = - 0.2

Answer 8

try to check bbc.co.uk/bitesize

4/x +x = 6/4 - 3
4/x+x/1 = 6/4 - 3/1
4x-x/x = 6-12
3x/x = -6
x= -2

Answer 9

This is not an answer but an observation. Now I know why I hated algebra at school and at 84 i still can't make head or tail of it

Answer 10

Jdn is correct