How do you solve #- 7< 5 - 2y <= 1?#

2 Answers
Jun 25, 2018

Answer:

Shown below

Explanation:

Treat it like a normal linear equation question:

#-7< 5-2y <=1 #

Get rid of the #5# in the middle by -5 on each of the terms

#-7 color(red)(" "-5 ) < 5 -2y color(red)(" "-5) <= 1color(red)( " "-5) #

#=> -12 < -2y <= -4 #

Divide each term by -2 to isolate #y#

When you divide by a negative number, the inequalities swap

#=> 6>y>=2 #

#=> color(blue)( 2 <= y < 6 ) #

Jun 25, 2018

Answer:

#y in [2,6)#

Explanation:

we have
#-7<5-2y<=1#
subtracting 5 on both sides
#-12<-2y<=-4#
dividing 2 both sides
#-6<-y<=-2#
multiplying -1 both sides
#6>y>=2#
we get a range of y such that greater than equal to 2 and less than 6 also
hence #y in[2,6)#