|x-20|<0.75

Question

Help metcrcrcrcrctyyyyyyyyyuuujhhhhhhhhhggggfffff

Answer 1

Hey, Jack!  Moaning won't help.    "When the going gets tough, the tough get going!"

 

Let's read the problem:   The absolute value of the quantity x minus 20 is less than 0.75

 

Absolute values cannot be negative.

 

The goal of this problem is to solve for x (alone) by putting all the numbers on the other side of the inequality.

 

So, here goes:

   The quantity (x-20)  is between -0.75 and 0.75 on the number line, right?  (small numbers on either side of 0)

                         -0.75 < (x-20) < 0.75

This is two situations combined and both have to be true.

                      - 0.75 < x -20      and       x-20 < 0.75

 

With inequalities, we can add the same amount to both sides and keep the same inequality.

                       19,25 < x       and        x < 20.75

 

Now, I'd encourage to draw that interval on a number line and try a value inside that range.  For example, x=20 is in that line segment, so is the absolute value of (20-20) less than 0.75?    YES !