Question

How do you solve `(x+2)/2=(x-6)/10`?

Answer 1

x = -4

Explanation:

We can multiply both sides of the equation by the `color(blue)"lowest common multiple (L.C.M)"` of 2 and 10, that is 10.

`cancel(10)^5xx((x+2))/cancel(2)^1=cancel(10)^1xx ((x-6))/cancel(10)^1`

which simplifies to.

`5(x+2)=x-6`

distribute :`5x + 10 = x - 6`

collect terms in x to the left and numeric terms to the right.

`rArr5x-x=-6-10rArr4x=-16`

Finally divide both sides by 4

`(cancel(4)^1 x)/cancel(4)^1=(-cancel(16)^4)/cancel(4)^1`

`rArrx=-4`
`color(magenta)"-----------------------------"`

Alternatively we can use the method of `color(blue)"cross-multiplication"`

`color(red)"x + 2"/color(blue)"2"=color(blue)"x - 6"/color(red)"10"`

multiply the same colour terms across the fraction (X)

`rArrcolor(red)"10(x+2)"=color(blue)"2(x-6)"`

distribute brackets : 10x + 20 = 2x - 12

collect terms in x to the left and numeric terms to the right.

`rArr10x-2x=-12-20rArr8x=-32`

Finally divide both sides by 8

`(cancel(8)^1 x)/cancel(8)^1=(-cancel(32)^4)/cancel(8)^1`

`rArrx=-4`
`color(magenta)"--------------------------"`