Question

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

Answer 1

`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`

`(-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 `x` to be smaller than `7`. It's obvious that any positive value of `x` will satisfy this equation, since

`-x <0" ",AAx>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

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

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

`x > color(green)(-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.

`(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 `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]}