First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:
#color(red)(3)(y + 1) - 4y >= -5#
#(color(red)(3) xx y) + (color(red)(3) xx 1) - 4y >= -5#
#3y + 3 - 4y >= -5#
Next, group and combine like terms on the left side of the inequality:
#3y - 4y + 3 >= -5#
#(3 - 4)y + 3 >= -5#
#-1y + 3 >= -5#
#-y + 3 >= -5#
Then, subtract #color(red)(3)# from each side of the inequality to isolate the #y# term while keeping the inequality balanced:
#-y + 3 - color(red)(3) >= -5 - color(red)(3)#
#-y + 0 >= -8#
#-y >= -8#
Now, multiply each side of the inequality by #color(blue)(-1)# to solve for #y# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#color(blue)(-1) xx -y color(red)(<=) color(blue)(-1) xx -8#
#y color(red)(<=) 8#