How do you solve (x+2)/2=(x-6)/10x+22=x−610?
1 Answer
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)"--------------------------"
