How many possible integer values are there for x if |4x - 3| < 6 ?
What I did here was to separate two scenarios:
a. 4x – 3 < 6 and
b. 4x – 3 > - 6
I simplified x in both scenarios that I ended up in a range of -2.25 < x < .75
Therefore, my answer is 3 integers (-2, -1, 0)
I would like to know if this method is correct and if I should use such method for problems that involve absolute value and inequality.
You can try algebraically, If x>=0, then you will have the range 0<=x<9/4
If x<0, you get x>3/4 but this solution is not valid so x must vbe x>=0. Hence, you have 3 integer solutions from the above inequality: 0, 1 and 2.
Hope this helps