# How do you solve and write the following in interval notation: 20x + 28 <=4( 4x + 5) ?

Dec 8, 2017

See a solution process below:

#### Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

$20 x + 28 \le \textcolor{red}{4} \left(4 x + 5\right)$

$20 x + 28 \le \left(\textcolor{red}{4} \times 4 x\right) + \left(\textcolor{red}{4} \times 5\right)$

$20 x + 28 \le 16 x + 20$

Next, subtract $\textcolor{red}{28}$ and $\textcolor{b l u e}{16 x}$ from each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$20 x - \textcolor{b l u e}{16 x} + 28 - \textcolor{red}{28} \le 16 x - \textcolor{b l u e}{16 x} + 20 - \textcolor{red}{28}$

$\left(20 - \textcolor{b l u e}{16}\right) x + 0 \le 0 - 8$

$4 x \le - 8$

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

$\frac{4 x}{\textcolor{red}{4}} \le - \frac{8}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} \le - 2$

$x \le - 2$

Or, in interval notation:

$\left(- \infty , - 2\right]$