|4x - 3| < 12 is equivalent to ?

Question

possible solutions...

-9/4 < x < 15/4

-15/4 < x < 9/4

-8/3 < x < 16/3

-16/3 < x < 8/3

Answer 1

-9/4 < x < 15/4

you can either have:

4x-3 < 12 which means 4x < 15

or

-(4x-3) < 12 which means -4x+3<12
so -4x<9 and 4x>-9

now try x=0

|4x - 3| <12 when x=0 so x=0 is a solution
and x is between -9/4 and 15/4

Answer 2

-15/4 < x < 9/4 and -16/3 < x < 8/3 both work, the two other possible answers don't.

Answer 3

|4x - 3| < 12

First, we translate this. Note that if |x| < a, then
-a < x < a. That's exactly what we do for this.

-12 < 4x - 3 < 12

We want to isolate the x within the inequality. To do this, we first add 3 to the inequality (which will get rid of the -3)

-12 + 3 < 4x < 12 + 3

Now, we simplify

-9 < 4x < 15

And now, we divide the inequality by 4.

(-9/4) < x < (15/4)

Answer 4

4x-3<(-12) . . . . .and . . . .4x-3<12
4x<(-9) . . . . . . . . . .. . . . .4x<15
x<(-9)/4 . . . . . .and .. . . . .x<15/4

. . . (-9)/4