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

Aug 8, 2015

$5 < y < 15$

#### Explanation:

$3 > 10 - 2 y + 3 > - 17$ Distribute the $2$ in $2 \left(5 - y\right)$

$3 > 13 - 2 y > - 17$ Combine like terms

$- 10 > - 2 y > - 30$ 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 $y < 15$

Aug 8, 2015

$5 < y < 15$

#### Explanation:

You can split the given inequality into two simpler inequalities :)

from $3 > 2 \left(5 - y\right) + 3 > - 17$

we can get
$3 > 2 \left(5 - y\right) + 3$
and
$2 \left(5 - y\right) + 3 > - 17$

then solving each...

$3 > 2 \left(5 - y\right) + 3$ [distribute the 2]
$3 > 10 - 2 y + 3$ [add like terms (the 10 and 3)]
$3 > 13 - 2 y$ [add 2y to both sides]
$2 y + 3 > 13$ [now subtract 3 from both sides]
$2 y > 10$ [finally, divide both sides by 2 to get y all alone]
$y > 5$

$2 \left(5 - y\right) + 3 > - 17$ [first distribute the 2]
$10 - 2 y + 3 > - 17$ [add like terms]
$13 - 2 y > - 17$ [add 2y to both sides]
$13 > 2 y - 17$ [add 17 to both sides]
$13 + 17 > 2 y$ [simplify]
$30 > 2 y$ [finally, divide both sides by 2]
$y < 15$

so we get
$y > 5$
and
$y < 15$