Multiplying both sides by 4 gives us:

(Note the change in sense due to dividing by a negative number).

Check: Taking x = 0 (which should work):

LHS = 3/2(1 − 0) = 3/2

RHS = 1/4

It is TRUE that 3/2 > 1/4, so that is good.

Now we take x = 3 (a convenient number bigger than 5/2, which should not work):

LHS = 3/2(1 − 3) = -3

RHS = 1/4 − 3 = -2 3/4

It is NOT true that -3 > -2 3/4 and so x = 3 fails, as we hoped.

We can be sure our answer (x < 5/2) is correct.