# How do you solve the inequality 7a<12a+10?

Jul 11, 2017

$- 2 < a$

#### Explanation:

Treat the inequality as an equals sign and solve normally. Be careful when dividing by a negative number but apart from that you're good to go!

Jul 12, 2017

$a > - \frac{12}{5}$

$a > - 2 \frac{1}{2}$

#### Explanation:

$7 a < 12 a + 10$

Treat an inequality in the same way as an equation. However if you multiply or divide by a negative number, the inequality sign will change around.

Therefore, try to keep the variable terms positive to avoid this.

Transposing the inequality can lead to:

$7 a - 12 a < 12 \text{ or } - 12 < 12 a - 7 a$

$\textcolor{red}{- 5 a <} 12 \text{ or } \textcolor{b l u e}{- 12 < 5 a} \leftarrow$ this one is preferable
$\textcolor{w h i t e}{x \ldots . x} \downarrow$
$\textcolor{red}{\frac{- 5 a}{- 5} >} \frac{12}{- 5} \text{ or } \textcolor{b l u e}{- 12 < 5 a}$

$\textcolor{red}{a} > - \frac{12}{5} \text{ or } \textcolor{b l u e}{- \frac{12}{5} < \frac{5 a}{5}}$

$\textcolor{b l u e}{- \frac{12}{5} < a} \text{ }$ can also be written as $a > - \frac{12}{5}$

$a > - 2 \frac{1}{2}$