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

##### 1 Answer

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)"-----------------------------"#

Alternativelywe 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)"--------------------------"#