That won't change the inequality.

But when you invert both sides of an inequality, you switch the inequality, right?

And that's one of the distinctions of an inequality.

So we have this inequality.

So that is our inequality.

So the inequality will switch.

So if I'm inverting all of the sides of this inequality, I have to switch the inequality signs.

And remember, when you multiply or divide both sides of an inequality by a negative, you swap the inequality.

So we have this inequality.

You have this inequality right there.

And when you multiply both sides of an inequality by a negative number or divide both sides by a negative number, you swap the inequality.

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the system for reconciling disparate parts.

You don't do anything to the inequality

It does not satisfy that inequality.

Now we're gonna divide both sides of this equation by 13.

We're actually injecting contrast into the organ.

If we pick one of these numbers, it's going to satisfy that inequality.

That doesn't change the inequality as long as we're subtracting the same value.

Now we can divide both sides of this inequality by 5 and we don't have to swap the inequality because we're dividing by a positive number and so we get z is less than 20 over 5.

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So this is the interval notation for this compound inequality right there.

No reason to change the inequality just yet.

So the inequality is 2 times x plus 6 is less than or equal to 8x.

So let's just try to isolate x on one side of this inequality.

Because if we pick one of these numbers, it's going to satisfy this inequality.

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In the inequalities, there's a whole set of x's that will satisfy this inequality.

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Las Vegas, we just solve for I on this inequalty.

And since we divided by a negative number, we swap the inequality.

We can divide both sides of this inequality by 3.

Once again, no reason to change the inequality just yet.

Alright? We could have done this equation in a slightly different way

And we exclude negative 2 by drawing an open circle at negative 2, but all the values greater than that are valid x's that would solve, that would satisfy this inequality.

So we could add a to both sides of this equation and it will not change the inequality.

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So the inequality stays the same as in our original problem.

It's only when you multiply by negatives that you swap the inequality.

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Now you can see it start. We're injecting the contrast into the organ into this decellularized liver.

So where do you go putting all of these disparate pieces together?

I'm just multiplying both sides of the inequality by the inverse of 5, because this will cancel out with 5 and will leave me just with C. Now I didn't draw the inequality here, because we have to remember if we multiply or divide both sides of an inequality by a negative number, you have to flip the inequality and we are doing that.

As long as you add or subtract the same value to both sides, it will not change the inequality.