I don't understand my problems. It says Find 4 more values for |9x-4| < x and I already found 1/2 and 2/5 for x.

Question

Here is the question exactly.

Find 4 more values for |9x-4| < x

Find all values for |9x-4| < x

 

Answer 1

Removing the absolute values:

 

9x - 4 < x    AND 9x - 4 > -x

 

9x - 4 - x < 0    AND 9x - 4 + x > 0

 

8x - 4 < 0    AND 10x - 4 > 0

 

x < 1/2  AND x > 4/10 = 2/5

 

So the interval is (2/5, 1/2) = (0.4, 0.5)

 

So any number in that interval will work.

 

For example, 4 values can be 0.425, 0.45, 0.475 , 0.48