anonymous
  • anonymous
Solve the inequality |x-10| - 9 < -1 and graph The solutions. Then write the solutions as a comp
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
As a compound inequality.
anonymous
  • anonymous
Pleaseeee helpppp!!!!
anonymous
  • anonymous
Do you know the first steps to solve the inequality?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.