# How do you solve and write the following in interval notation: -2(x-1)-12<2(x+1)?

Jul 8, 2017

See a solution process below:

#### Explanation:

First, expand the terms on both sides of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{- 2} \left(x - 1\right) - 12 < \textcolor{b l u e}{2} \left(x + 1\right)$

$\left(\textcolor{red}{- 2} \times x\right) - \left(\textcolor{red}{- 2} \times 1\right) - 12 < \left(\textcolor{b l u e}{2} \times x\right) + \left(\textcolor{b l u e}{2} \times 1\right)$

$- 2 x - \left(- 2\right) - 12 < 2 x + 2$

$- 2 x + 2 - 12 < 2 x + 2$

$- 2 x - 10 < 2 x + 2$

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

$\textcolor{red}{2 x} - 2 x - 10 - \textcolor{b l u e}{2} < \textcolor{red}{2 x} + 2 x + 2 - \textcolor{b l u e}{2}$

$0 - 12 < \left(\textcolor{red}{x} + 2\right) x + 0$

$- 12 < 4 x$

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

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

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

$- 3 < x$