How do you solve (x+2)/2=(x-6)/10x+22=x610?

1 Answer
Jul 17, 2016

x = -4

Explanation:

We can multiply both sides of the equation by the color(blue)"lowest common multiple (L.C.M)"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)"--------------------------"