# How do you solve the inequality -n/3 - 5<-4?

May 2, 2016

$n > - 3$

#### Explanation:

$- \frac{n}{3} + 0 < - 4 + 5$

$- \frac{n}{3} < 1$

Multiply both sides by 3

$- n < 3$ ...............................(1)

Add $n$ to both sides

$0 < 3 + n$

Subtract 3 from both sides

$- 3 < n$

$n > - 3$
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Reconsider inequality (1)

Shortcut method
Multiply by (-1) and turn the inequality round the other way

$\implies \left(- 1\right) \left(- n < 3\right) \to \text{ } n > 3$