# How do you solve 2-3(x+2)<11?

Aug 11, 2016

$x > - 5$

#### Explanation:

Treat inequalities in the same way as an equation, unless you multiply or divide by a negative number, in which case the inequality sign will change around.

$2 - 3 \left(x + 2\right) < 11 \text{ remove brackets}$

$2 - 3 x - 6 < 11 \text{ the x-term is negative}$

Either:$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .}$ Or

$\textcolor{red}{- 4 - 11 < 3 x} \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \textcolor{b l u e}{- 3 x < 11 - 2 + 6}$

$\textcolor{red}{- 15 < 3 x} \text{ } \div 3 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots .} \textcolor{b l u e}{- 3 x < 15}$

$\textcolor{red}{- 5 < x} \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} \textcolor{b l u e}{\frac{- 3 x}{- 3} > \frac{15}{- 3}} \text{ } \div - 3$

$\textcolor{red}{\Rightarrow x > - 5} \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \textcolor{b l u e}{x > - 5}$