Question

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

Answer 1

`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`

Answer 2

`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`