How do you solve the inequality: #3 > 2 (5-y) + 3 > -17#?

2 Answers
Babette
Aug 8, 2015

#5 < y < 15#

Explanation:

#3 > 10-2y+3> -17# Distribute the #2# in #2(5-y)#

#3 >13-2y> -17# Combine like terms

#-10> -2y> -30# Subtract 13 from everything

#5< y < 15# Divide through by #-2#

Remember that the inequality flips when dividing by a negative number.

Or written another way

#y> 5# and #y<15#

jigglypuff314
Aug 8, 2015

#5 < y < 15#

Explanation:

You can split the given inequality into two simpler inequalities :)

from #3 > 2(5-y)+3> -17#

we can get
#3>2(5-y)+3#
and
#2(5-y)+3> -17#

then solving each...

#3>2(5-y)+3# [distribute the 2]
#3>10-2y+3# [add like terms (the 10 and 3)]
#3>13-2y# [add 2y to both sides]
#2y + 3 > 13# [now subtract 3 from both sides]
#2y > 10# [finally, divide both sides by 2 to get y all alone]
#y > 5#

#2(5-y)+3> -17# [first distribute the 2]
#10-2y+3> -17# [add like terms]
#13 - 2y > -17# [add 2y to both sides]
#13 > 2y - 17# [add 17 to both sides]
#13+17 > 2y# [simplify]
#30>2y# [finally, divide both sides by 2]
#y < 15#

so we get
#y > 5#
and
#y < 15#

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