|m-1| > 2 replacement set: [-3,-1,0,1,3]

Question

Look at the inequality below. Without solving it, explain which numbers from the given replacement set are reasonable solutions. 

Answer 1

Your instructions merely mean this: in succession, plug in each of the numbers listed in the 'replacement set.'

 

Then see if the absolute value that you get exceeds 2.  For each instance where this inequality is true, you have a solution, otherwise not.

Answer 2

l m-1 l means:  the distance between m-1 and 0 on the number line.

 

So, l m-1 l > 2 means that m-1 is more than 2 units from 0 on the                               number line.

 

Therefore, m-1>2 or m-1<-2

 

So, m>3 or m<-1

 

Of the 5 given numbers, only -3 is a solution of the given inequality.