Solve:||x-3|-2|≤1
Please show work!
Thanks

Step-by-step explanation:

Hello,

We know that

So we need to take into account two cases

Case 1 -

Then, |x-3|=x-3

||x-3|-2|=|x-3-2|=|x-5|

Either x-5 is positive and then |x-5|=x-5 and

Or x-5 is negative and then, |x-5|=-x+5

So the solution is [4;6]

Case 2 -

Then, |x-3|=-x+3

||x-3|-2|=|-x+3-2|=|-x+1|

Either -x+1 is positive and then |-x+1|=-x+1 and

Or -x+1 is negative and then, |-x+1|=x-1

So the solution is [0;2]

Conclusion

The solution is [0;2]∪[4;6]

Thanks

correct answers below:

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )