# How do you solve and write the following in interval notation: -4x< -16 and x+ 4 > 5?

Jul 21, 2017

See a solution process below:

#### Explanation:

Solution To Inequality 1

$- 4 x < - 16$

We will divide each side of the inequality by $\textcolor{b l u e}{- 4}$ to solve for $x$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

$\frac{- 4 x}{\textcolor{b l u e}{- 4}} \textcolor{red}{>} \frac{- 16}{\textcolor{b l u e}{- 4}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 4}}} x}{\cancel{\textcolor{b l u e}{- 4}}} \textcolor{red}{>} 4$

$x > 4$

Solution To Inequality 2

$x + 4 > 5$

We will subtract $\textcolor{red}{4}$ from each side of the equation to solve for $x$ while keeping the equation balanced:

$x + 4 - \textcolor{red}{4} > 5 - \textcolor{red}{4}$

$x + 0 > 1$

$x > 1$

The Solutions Are: $x > 1$ and $x > 4$

However, because the interval $\left(1 , 4\right)$ is a valid solution for Inequality 2 but not for inequality 1 the solution is:

$x > 4$

Interval notation:

$\left(4 , + \infty\right)$