lxl + 5 <= 1

Question

lxl + 5 ≤ 1

Answer 1

Dear Mark,

     What you notice right off is that a positive number added to 5 can not be less than one, nor can it be nor equal to one.  However, let's see this inequality worked out anyway to find out what happens:

 

lXl  + 5 ≤ 1          Let's get the absolute value of X by itself.  Therefore, subtract 5 from both sides.

 

 

lXl +5 -5≤ 1-5      Simplify.

 

 

lXl ≤ -5                Here you can see that something is wrong, but continue the process.  Divide inequality into two parts:

 

X≥5  and     X≤-5      Now, substitute some values that are supposed to work back into the original inequality.

 

 

Try 5 because you have that X≥5.       l5l + 5 ≤1        5+ 5≤1       10≤1    False statement

 

Next, try -5.                                      l-5l + 5 ≤1         5 +5≤1      10≤1   False statement

 

I hoped that I have helped.  If I have helped you, please give me a thumbs up.

                                                     Susan C.

 

 

 

Answer 2

lxl is always nonnegative , so lxl+5 ≥ 5.  

 

Therefore, the inequality lxl + 5 ≤ 1 has no solution.