First, group and combine like terms on the left side of the equation:
#5y - 2y + 7 = 2(y + 3) + 1#
#(5 - 2)y + 7 = 2(y + 3) + 1#
#3y + 7 = 2(y + 3) + 1#
Next, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:
#3y + 7 = color(red)(2)(color(blue)(y) + color(blue)(3)) + 1#
#3y + 7 = (color(red)(2) xx color(blue)(y)) + (color(red)(2) xx color(blue)(3)) + 1#
#3y + 7 = 2y + 6 + 1#
#3y + 7 = 2y + 7#
Now, subtract #color(red)(7)# and #color(blue)(2y)# from each side of the equation to solve for #y# while keeping the equation balanced:
#3y - color(blue)(2y) + 7 - color(red)(7) = 2y - color(blue)(2y) + 7 - color(red)(7)#
#(3 - color(blue)(2))y + 0 = 0 + 0#
#1y = 0#
#y = 0#
