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

Question

Ethan Adkins · Accepted Answer

x = -4

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

Jace Anderson · Answer

undefined To solve the equation (x+2)/2=(x-6)/10, you can follow these steps:

1. Multiply both sides of the equation by 2 and 10 to eliminate the denominators.
2. Expand the equation.
3. Simplify and solve for x.

The solution to the equation is x = 14.