How do you solve #2y+6<2(y+7)#?

1 Answer
smendyka
May 21, 2017

See a solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying each of the terms within the parenthesis by the term outside the parenthesis:

#2y + 6 < color(red)(2)(y + 7)#

#2y + 6 < (color(red)(2) * y) + (color(red)(2) * 7)#

#2y + 6 < 2y + 14#

Next, subtract #color(red)(2y)# from each side of the inequality:

#-color(red)(2y) + 2y + 6 < -color(red)(2y) + 2y + 14#

#0 + 6 < 0 + 14#

#6 < 14#

Because 6 is in fact less than 14 the solution to this inequality is #y# can be any number and this inequality will be true. Therefore the solution is #y = {RR}#

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