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

##### 1 Answer

#### Explanation:

You can solve this inequality by isolating

#(-color(red)(cancel(color(black)(2)))x)/color(red)(cancel(color(black)(2))) < 14/2#

#-x < 7#

Now take a look at how the inequality looks like. You need **minus** *positive* value of

#-x <0" ",AAx>0#

This is true for *some* negative values of **bigger** than *smaller* than

#-(-8) < 7 implies 8 color(red)(cancel(color(black)(<))) 7#

This means that *any* value of **greater than**

#x > color(green)(-7)#

This is why when you divide both sides ofan inequality by **flip** the inequality sign.

#(color(red)(cancel(color(black)(-1)))x)/color(red)(cancel(color(black)(-1))) color(green)(>) 7/(-1)#

#x > -7#

To graph the solution set for this inequality, draw a **dotted** vertical line parralel to the *right* of the dotted line.

The fact that the line is dotted indicates that

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