# How do you solve 14- 4k < 38?

Mar 10, 2018

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{14}$ from each side of the inequality to isolate the $k$ term while keeping the equation balanced:

$14 - \textcolor{red}{14} - 4 k < 38 - \textcolor{red}{14}$

$0 - 4 k < 24$

$- 4 k < 24$

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

$\frac{- 4 k}{\textcolor{b l u e}{- 4}} \textcolor{red}{>} \frac{24}{\textcolor{b l u e}{- 4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 4}}} k}{\cancel{\textcolor{b l u e}{- 4}}} \textcolor{red}{>} - 6$

$k \textcolor{red}{>} - 6$

Mar 10, 2018

$k > - 6$

#### Explanation:

We can treat this inequality like it's an equation. If our problem was instead $14 - 4 k = 38$, we would subtract $14$ from both sides. We would do the same here to get:

$- 4 k < 24$

Now, we divide both sides by $- 4$, and here's the catch: Since we're dividing the inequality by a negative number, the direction of the sign will flip. This would even hold true of we're multiplying. We get:

$k > - 6$

Mar 10, 2018

$k > - 6$

#### Explanation:

$14 - 4 k < 38$

Start by subtracting $14$ on both sides

$14 - 4 k - 14 < 38 - 14$

$- 4 k < 24$

Divide both sides by $- 4$
$\frac{\cancel{- 4} k}{\cancel{- 4}} < \frac{24}{- 4}$

$k > - 6$

Note:

When you are solving an inequality, if you divide both sides by a negative sign, you MUST change the sign as well. If it was $<$, it will be $>$. Got it?