start by isolating x
[tex]4x + y < 2 \\ 4x + y - y < 2 - y \\ 4x < 2 - y \\ \frac{1}{4} \times 4x < (2 - y) \times \frac{1}{4} \\ x < \frac{2 - y}{4} [/tex]
now, if y>-2 what is the biggest number 2-y can be?
well, as y gets more towards 0 from the negative side, we have
[tex]2 - ( - 2) = 4 \\ 2 - ( - 1.5) = 3.5 \\ 2 - ( - 1) = 3 \\ 2 - ( - .5) = 2.5 \\ 2 - (0) = 2[/tex]
as it gets positive we have
[tex]2 - .5 = 1.5 \\ 2 - 1 = 1 \\ 2 - 1.5 = .5 \\ 2 - 2 = 0 \\ 2 - 2.5 = - .5[/tex]
it keeps getting smaller!
so the biggest it could be is 4!
[tex] \frac{4}{4} = 1[/tex]
so, x<1
