WHY We Flip the Inequality Sign After Multiplying or Dividing by a Negative Number

You've probably been switching your inequality sign whenever you multiply or divide by a negative number. Good job. But WHY do we do this? Watch the video to see why and what happens if we don't flip the sign.

#midnightmathtutor #inequalities #graphinginequalities

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[vespirited]

Another way to think about it would be to visualize the number line.

-x < -5 implies that x lies to the left of -5. But as we cross 0 on the number line and move from the negative side to the positive side, we'd flip our numbers around, so x would lie on the right of 5.

If we take x to be 7 for example, -7 is less than -5, and 7 is greater than 5

[TechnoGuyGameGod]

Hey Chelsea, I wanted to let you know that your videos have really been helping out my little brother!
I love how organised your video are - clearly explaining stuff.

[Awesome-ctvr]

I like to explain it with an analytic system.
Every algebratic equation has a representation on a graph.

In that case its a linear equation.
And you looking to find some region of that line where its x fits for some y value.

When you multiply or divide by minus 1.
You flip the m (slope).
And flip the y value too.

So basicly you mirrored your whole graph when you did it.
Try to take a paper and draw a graph with a line.
Color part of that line. Now take the paper and face it to the mirror. (Like multiplying by -1.)
The region youre looking for is the otherway around now.
Therefor the inequallity sign will flip to keep the equation true after flipping the graph.