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As a compound inequality.
Do you know the first steps to solve the inequality?
No not sure
First step, is to isolate the absolute value side!
How do u exactly do that
By removing everything that's not INSIDE the absolute value sign on the left side of the inequality!
So u remove the -9 < -1?
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: <
Do do I cross out the -9?
No you can't just make the -9 disappear into nothing.
You have to add it to both sides!
So what do we do with the -9 to get rid of it?
You have to add 9 to the left side and the right side. |x-10| - 9 < -1 + 9 +9
By adding the opposite of -9 you can cancel it out with itself!
So it would be 8?
Yes! It would be 8 on the right side!
So now do we work within the absolute value on the left side?
So now we have |x-10| < 8 and now the absolute value sign has been isolated!
Yes but you have to do something special to solve that absolute value. Do you know what's next?
Ok so now what's the next step
Now you have to break the absolute value into "cases".
How will we do that?
|x-10| < 8 is broken down into x-10 < 8 and x-10 > -8|dw:1440964722548:dw|
Notice how i didn't include the absolute value signs, and how the second one has the negative 8!!
Why does it turn to -8?
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!
See how < became > on the second one?
U always have to do that?
We do this in order to solve absolute value inequalities. And yes you always have to do that.
Now do we subtract the x-10
But ONLY if you have absolute values in your inequality!
no just the -10 leave the x where it is
So x-10 < 8 +10 +10
So for the next step the x disappears?
No we're trying to find what X is. Oh and by the way the 2 cases have nothing to do with each other!
They are 2 different problems now
I thought the new sign was >
Only on the second case!
We are working with the first case where everything stays the same!
If you do the second case you get x-10 > -8 +10 +10 x > 2
So now we have the first case: x < 18 and the second case: x > 2
We're still doing the first case right
No the first and second ones are right there
First Case: x < 18 Second case: x > 2
See how they both have x? Couldn't we just write it like this then: 2 < x < 18 And that's your compound inequality!