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

Feb 18, 2017

First, expand the terms within parenthesis by multiplying each term with the parenthesis by the term outside the parenthesis:

$\left(\textcolor{red}{2} \times x\right) - \left(\textcolor{red}{2} \times 3\right) < \left(\textcolor{red}{3} \times 2 x\right) + \left(\textcolor{red}{3} \times 2\right)$

$2 x - 6 < 6 x + 6$

Next, subtract $\textcolor{red}{2 x}$ and $\textcolor{b l u e}{6}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$2 x - 6 - \textcolor{red}{2 x} - \textcolor{b l u e}{6} < 6 x + 6 - \textcolor{red}{2 x} - \textcolor{b l u e}{6}$

$2 x - \textcolor{red}{2 x} - 6 - \textcolor{b l u e}{6} < 6 x - \textcolor{red}{2 x} + 6 - \textcolor{b l u e}{6}$

$0 - 12 < 4 x + 0$

$- 12 < 4 x$

Now, divide each side of the inequality by $\textcolor{red}{4}$ to solve for $x$ while keeping the inequality balanced:

$\frac{- 12}{\textcolor{red}{4}} < \frac{4 x}{\textcolor{red}{4}}$

$- 3 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}}$

$- 3 < x$

To put the solution in terms of $x$ we can reverse or "flip" the inequality:

$x > - 3$