# How do you solve -p-4p> -10?

Nov 21, 2016

$p \setminus < 2$

#### Explanation:

equation
$- p - 4 p \setminus > - 10$

concepts applied
if $- a \left(b\right) \setminus > c$, then $b \setminus \textcolor{red}{\setminus <} \frac{c}{-} a$

calculation
add like terms $\Rightarrow - 5 p \setminus > - 10$
divide both sides by -5 $\Rightarrow \frac{\setminus \cancel{- 5} p}{\setminus} \cancel{\setminus \textcolor{o l i v e}{- 5}} \setminus \textcolor{red}{\setminus <} \frac{- 10}{\setminus} \textcolor{o l i v e}{- 5}$
simplify division $\Rightarrow p \setminus < 2$

checking
plug in any value less than 2
-(1)-4(1)\stackrel{?}{\gt}-10
-1-4\stackrel{?}{\gt}-10
$- 5 \setminus > - 10$
correct!

Nov 21, 2016

$p < 2$

#### Explanation:

You can treat an inequality in the same way as an equation, unless to multiply or divide by a negative number, in which case the inequality sign will change around.

Let's swop the negative terms onto the other sides.

$- p - 4 p > - 10 \text{ } \leftarrow$ simplify the like terms

$- 5 p > - 10 \text{ } \leftarrow$ Add 5p to both sides

$- 5 p + 5 p > - 10 + 5 p \text{ } \leftarrow$ add 10 to both sides

$10 > 5 p \text{ } \leftarrow \div 5$

$2 > p \text{ } \leftarrow$ this means the same as:

$p < 2$

Note that the same result would have been obtained by dividing by $- 5$ and changing the inequality sign, as explained by another contributor.

$- 5 p > - 10$

$\frac{- 5 p}{-} 5 < \frac{- 10}{-} 5 \text{ } \leftarrow$ note the sign changes!

$p < 2$