# How do you solve and graph –2x < 14 ?

Aug 13, 2015

$x > - 7$

#### Explanation:

You can solve this inequality by isolating $x$ on one side, something that can be done by dividing both sides of the equation first by $2$

$\frac{- \textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} < \frac{14}{2}$

$- x < 7$

Now take a look at how the inequality looks like. You need minus $x$ to be smaller than $7$. It's obvious that any positive value of $x$ will satisfy this equation, since

$- x < 0 \text{ } , \forall x > 0$

This is true for some negative values of $x$ as well, more precisely for values of $x$ that are bigger than $x = - 7$. For values of $x$ that are smaller than $- 7$, you have

$- \left(- 8\right) < 7 \implies 8 \textcolor{red}{\cancel{\textcolor{b l a c k}{<}}} 7$

This means that any value of $x$ that is greater than $7$ will satisfy this inequality.

$x > \textcolor{g r e e n}{- 7}$

This is why when you divide both sides ofan inequality by $- 1$, like you would to isolate $x$, you must flip the inequality sign.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 1}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 1}}}} \textcolor{g r e e n}{>} \frac{7}{- 1}$

$x > - 7$

To graph the solution set for this inequality, draw a dotted vertical line parralel to the $y$-axis that goes through $x = - 7$. Since you want all values of $x$ that are greater than $- 7$, you must shade the area to the right of the dotted line.

The fact that the line is dotted indicates that $x = - 7$ is not part of the solution set.

graph{x> -7 [-10, 10, -5, 5]}