Given the inequality:

-4 < 3-4x < 12

We will solve the same way we solve for the equations.

We need to isolate x in the middle.

Then we will subtract 3 from all sides.

==> -4-3 < -4x < 12-3

==> -7 < -4x < 9

Now we will divide by -4 and reverse the inequality.

==> -7/-4 > x > -9/4

==> -9/4 < x < 7/4

Then x belongs to the interval ( -9/4, 7/4)

**==> x = ( -9/4 , 7/4).**

We have the inequation -4 < 3-4x < 12.

Now -4 < 3-4x

=> -4 -3 < -4x

=> -7 < -4x

=> 7 > 4x

=> (7/4) > x

3-4x < 12

=> -4x < 12 - 3

=> -4x < 9

=> -x < 9/4

=> x > -9/4

**Therefore we have (7/4) > x > (-9/4)**

-4 < 3-4x < 12 find x.

There are 3 inequalities:

-4 < 3-4x, or -4 < 12, or 3-4x < 12.

We take -4< 3-4x and 3-4x <12, as there is nothing to prove -4 < 12 which is a truth.

-4 < 3-4x.

=> 4x-4 < 3.

=> 4x < 3+4 = 7.

=> 4x/4 < 7/4 = 1.75.

So x < 1.75....(1)

We take the inequality: 3-4x < 12.

=> 3-12 < 4x.

=> -9< 4x

=> -9/4 < 4x/4.

=> -2.25 < x.........(2).

We combine the solutions (1) and(2): -2.25 < x < 1.75.