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

2 Answers
Rhys
Jun 25, 2018

Shown below

Explanation:

Treat it like a normal linear equation question:

-7< 5-2y <=1 −7<5−2y≤1

Get rid of the 55 in the middle by -5 on each of the terms

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

=> -12 < -2y <= -4 ⇒−12<−2y≤−4

Divide each term by -2 to isolate yy

When you divide by a negative number, the inequalities swap

=> 6>y>=2 ⇒6>y≥2

=> color(blue)( 2 <= y < 6 ) ⇒2≤y<6

IZUkuABA
Jun 25, 2018

y in [2,6)y∈[2,6)

Explanation:

we have
-7<5-2y<=1−7<5−2y≤1
subtracting 5 on both sides
-12<-2y<=-4−12<−2y≤−4
dividing 2 both sides
-6<-y<=-2−6<−y≤−2
multiplying -1 both sides
6>y>=26>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)y∈[2,6)

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