Solve:||x-3|-2|≤1
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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

step-by-step explanation:

a

step-by-step explanation: