Question

5 < k -2 < 11 ?

-4 > y + 2 > -10 ?
5 -m < 4 or 7m > 35 ?
3 < 2p -3 < 12 ?

Answer 1

`7 < k < 13`

`-6>y>-12`

`m > 5`

`3 < p < (15)/(2)`

Explanation:

Given

`5 < k -2 < 11`

`-4 > y + 2 > -10`

`5 -m < 4\ or\ 7m > 35`

`3 < 2p -3 < 12`

Required

Solve

Solving (1):

`5 < k -2 < 11`

The above can be represented as:

`5<k -2` and
`k -2<11`

Solving
`5<k -2`

`5 + 2 <k`

`7<k`

Solving
`k -2<11`

`k < 2 + 11`

`k < 13`

So, we have:

`7<k` and
`k < 13`

This can be combined as:

`7 < k < 13`

Solving (2):

`-4 > y + 2 > -10`

Split as:

`-4 > y + 2` and
`y + 2 > -10`

Solving
`-4 > y + 2`

`-4 - 2 > y`

`-6 > y`

Solving
`y + 2 > -10`

`y > -10 - 2`

`y > -12`

So, we have:

`-6 > y` and
`y > -12`

This gives

`-6>y>-12`

Solving (3):

`5 -m < 4\ or\ 7m > 35`

Solve for m in both cases:

`5 - m < 4`

`-m<4 - 5`

`-m<- 1`

`m > 1`

`7m > 35`

Divide both sides by 5

`m > 5`

So, we have:

`m > 1` or
`m > 5`

The solution is
`m > 5` because
`5> 1`

Solving (4):

`3 < 2p -3 < 12`

The above can be represented as:

`3 < 2p - 3` and
`2p - 3<12`

Solving
`3 < 2p - 3`

Add 3 to both sides

`3 + 3 < 2p - 3 + 3`

`6 < 2p`

Divide both sids by 2

`3 < p`

`2p - 3<12`

Add 3 to both sides

`2p - 3 + 3 < 12 + 3`

`2p < 12 + 3`

`2p < 15`

Solve for p

`p < (15)/(2)`

So, we have:

`3 < p` and
`p < (15)/(2)`

Combined as:

`3 < p < (15)/(2)`