Question 437859
To solve this inequality, we graph the linear equation {{{2x+4y=8}}}

To graph this linear equation we find the x and y-intercepts.

 To find the y-intercept we make x=0:{{{2*0+4y=8}}} => {{{y=2}}},we have (0, 2)

To find the x-intercept we make y=0:{{{2*x+4*0=8}}} => {{{x=4}}},we have (4, 0)

Plot these two points on coordinative system and draw the straight line through them as in figure.
To determine which half-plane is the solution we choose a test point (0,0) and plug it in the inequality:2*0+4*0<8 => 0<8,this point satisfy the inequality, therefore the half-plane which contain the point (0,0) is the solution.See the shadow area on the figure.

{{{graph(300, 300, -5, 10, -5, 7, 2x+4y<8)}}}