Question

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

Answer 1

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 )`

Answer 2

`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)`