# How do you solve the inequality 2(w+4)>7(w-1)?

Oct 3, 2016

$w < 3$

#### Explanation:

1. Expand both sides:
$2 \left(w + 4\right) = 2 w + 8$, and $7 \left(w - 1\right) = 7 w - 7$

2. Bring all the variables on the left side, and all the constants on the right:
$2 w + 8 > 7 w - 7 \setminus \implies 2 w - 7 w > - 7 - 8$

3. Sum the terms:
$- 5 w > - 15$

4. Divide both terms by $- 5$. Note that when you deal with an inequality, if you multiply/divide both terms by a negative number you need to switch the inequality sign:
$- 5 w > - 15 \setminus \implies w < \frac{- 15}{- 5} = 3$