How do you solve #3( y + 1) - 4y >= - 5#?

1 Answer
smendyka
Oct 3, 2017

See a solution process below:

Explanation:

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#

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