x + 2y > -2 is solved as follows:
subtract x from both sides of the equation to get:
2y > -2 + x
divide both sides of the equation by 2 to get:
y > (-2 + x) / 2
3x + y <= 3 is solved as follows:
subtract 3x from both sides of the equation to get:
y <= 3 - 3x
the 2 equations that you have modified so they can be graphed are:
y > (-2 + x) / 2
y <= 3 - 3x
the equations that you will graph are:
y = (-2 + x) / 2
y = 3 - 3x
those graphs will look like this:
the line that crosses the y-axis at y = 3 is the graph of the equation y = 3 - 3x.
the line that crosses the y-axis at y = -1 is the graph of the equation y = (-2 + x) / 2
now that you graphed the lines, you need to go back to the inequality equations and see what area you want to shade.
the inequality equations are:
y > (-2 + x) / 2
y <= 3 - 3x
you want to be above the line of the equation y = (-2 + x) / 2
you want to be below or on the line of the equation y = (3 - 3x)
you will need to show the line y = (-2 + x) / 2 as a dashed line because you will not be on the line, you will only be above it.
you will need to show the line y = 3 - 3x as a solid line because you will be on the line as well as below it.
the shaded area is shown in the picture of the graph shown below:
it is below and to the left of the line y = 3 - 3x.
it is above the line y = (-2 + x) / 2
it is only in the upper left section of the graph because that is the only section of the graph where both requirements are met.