Answer
y=-1
Work Step by Step
Simplifying
5(2y + -3) = 3(7y + -6) + 19(y + 1) + 14
Reorder the terms:
5(-3 + 2y) = 3(7y + -6) + 19(y + 1) + 14
(-3 * 5 + 2y * 5) = 3(7y + -6) + 19(y + 1) + 14
(-15 + 10y) = 3(7y + -6) + 19(y + 1) + 14
Reorder the terms:
-15 + 10y = 3(-6 + 7y) + 19(y + 1) + 14
-15 + 10y = (-6 * 3 + 7y * 3) + 19(y + 1) + 14
-15 + 10y = (-18 + 21y) + 19(y + 1) + 14
Reorder the terms:
-15 + 10y = -18 + 21y + 19(1 + y) + 14
-15 + 10y = -18 + 21y + (1 * 19 + y * 19) + 14
-15 + 10y = -18 + 21y + (19 + 19y) + 14
Reorder the terms:
-15 + 10y = -18 + 19 + 14 + 21y + 19y
Combine like terms: -18 + 19 = 1
-15 + 10y = 1 + 14 + 21y + 19y
Combine like terms: 1 + 14 = 15
-15 + 10y = 15 + 21y + 19y
Combine like terms: 21y + 19y = 40y
-15 + 10y = 15 + 40y
Solving
-15 + 10y = 15 + 40y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-40y' to each side of the equation.
-15 + 10y + -40y = 15 + 40y + -40y
Combine like terms: 10y + -40y = -30y
-15 + -30y = 15 + 40y + -40y
Combine like terms: 40y + -40y = 0
-15 + -30y = 15 + 0
-15 + -30y = 15
Add '15' to each side of the equation.
-15 + 15 + -30y = 15 + 15
Combine like terms: -15 + 15 = 0
0 + -30y = 15 + 15
-30y = 15 + 15
Combine like terms: 15 + 15 = 30
-30y = 30
Divide each side by '-30'.
y = -1
Simplifying
y = -1
