How do you solve #6y - 8 = 12 + 10y#?

Question

Avery Alexander · Accepted Answer

Expanded explanation

#color(red)("Objective is to have y, on its own, on one side of the = and everything else on the other side.")# Brackets are used to show previous part to help make things clearer about what is happening. .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Add 8 to both sides to remove it from the left.")# #(6y-8) + color(red)(8) = (12 + 10y) + color(red)(8)# #6y -8 + 8 = 12 +8 + 10y# #6y +0 = 20 + 10y# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Subtract 10y from both sides to remove it from the right.")# #(6y) - color(red)(10y) = (20+10y)-color(red)(10y)# #6y - color(red)(10y) = 20+10y-color(red)(10y)# #-4y = 20# We need the y part to be positive so multiply both sides by negative 1 # color(red)(-1) times (-4y) = color(red)(-1) times (20)# #4y =-20# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Divide both sides by 4 so that the 4 in front of 4y becomes 1. As 1 times anything is itself.")# #color(red)(1/4) times (4y) = color(red)(1/4) times (-20)# #1 times y = (-20)/4# #y= - 5#

Savannah Anderson · Answer

undefined To solve the equation 6y - 8 = 12 + 10y:

1. Subtract 6y from both sides: -8 = 12 + 4y.
2. Subtract 12 from both sides: -20 = 4y.
3. Divide both sides by 4: y = -5.