`3/2(1-x)>1/4-x`

Multiplying both sides by 4 gives us:

`6(1-x)>1-4x`

` 6-6x>1-4x`

`-6x+4x>1-6`

`-2x> -5`

`x<5/2`

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

Here's the graph of this solution:

12340-1-2-3-4x2.5Open image in a new page

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.