Solve the inequality |x-10| - 9 < -1 and graph The solutions. Then write the solutions as a comp

- anonymous

Solve the inequality |x-10| - 9 < -1 and graph The solutions. Then write the solutions as a comp

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- anonymous

As a compound inequality.

- anonymous

Pleaseeee helpppp!!!!

- anonymous

Do you know the first steps to solve the inequality?

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## More answers

- anonymous

No not sure

- anonymous

First step, is to isolate the absolute value side!

- anonymous

How do u exactly do that

- anonymous

By removing everything that's not INSIDE the absolute value sign on the left side of the inequality!

- anonymous

So u remove the -9 < -1?

- anonymous

Just the -9 because the -1 is on the right side of the inequality.
When I say inequality i mean the symbol in the middle that looks like this: <

- anonymous

Do do I cross out the -9?

- anonymous

No you can't just make the -9 disappear into nothing.

- anonymous

You have to add it to both sides!

- anonymous

So what do we do with the -9 to get rid of it?

- anonymous

You have to add 9 to the left side and the right side.
|x-10| - 9 < -1
+ 9 +9

- anonymous

By adding the opposite of -9 you can cancel it out with itself!

- anonymous

So it would be 8?

- anonymous

Yes! It would be 8 on the right side!

- anonymous

So now do we work within the absolute value on the left side?

- anonymous

So now we have |x-10| < 8 and now the absolute value sign has been isolated!

- anonymous

Yes but you have to do something special to solve that absolute value. Do you know what's next?

- anonymous

Ok so now what's the next step

- anonymous

Multiply?

- anonymous

Now you have to break the absolute value into "cases".

- anonymous

How will we do that?

- anonymous

|x-10| < 8 is broken down into x-10 < 8 and x-10 > -8|dw:1440964722548:dw|

- anonymous

Notice how i didn't include the absolute value signs, and how the second one has the negative 8!!

- anonymous

Why does it turn to -8?

- anonymous

For the first "case" just rewrite the original problem. For the second "case" make everything on the right the opposite sign AND flip the inequality sign!

- anonymous

See how < became > on the second one?

- anonymous

U always have to do that?

- anonymous

We do this in order to solve absolute value inequalities. And yes you always have to do that.

- anonymous

Now do we subtract the x-10

- anonymous

But ONLY if you have absolute values in your inequality!

- anonymous

no just the -10 leave the x where it is

- anonymous

So
x-10 < 8
+10 +10

- anonymous

So for the next step the x disappears?

- anonymous

No we're trying to find what X is. Oh and by the way the 2 cases have nothing to do with each other!

- anonymous

They are 2 different problems now

- anonymous

I thought the new sign was >

- anonymous

Only on the second case!

- anonymous

We are working with the first case where everything stays the same!

- anonymous

Oh ok

- anonymous

If you do the second case you get x-10 > -8
+10 +10
x > 2

- anonymous

So now we have the first case: x < 18 and the second case: x > 2

- anonymous

We're still doing the first case right

- anonymous

No the first and second ones are right there

- anonymous

First Case: x < 18
Second case: x > 2

- anonymous

See how they both have x? Couldn't we just write it like this then: 2 < x < 18 And that's your compound inequality!

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