Answer:
The last option.
Step-by-step explanation:
Inequalities are equations for which a range of solutions is possible. We graph these as a normal line would be graphed. We use special markings to determine the solution possibilities.
- Inequalities with equal to as part of the solution are drawn with solid lines. (Those without are drawn with dashed lines.) Each of these has solid lines.
- Inequalities are then testes by inputting a coordinate point into the equation and determining if it is true. If true, we shade everything on that side of the line. If false, we shade everything on the other side.
- In a system (multiple inequalities), the shaded areas which are overlapping are the solution.
In this problem, we are finding the solutions for y greater than or equal to 3, y less than or equal to x, and y less than -1/2 times x +8.
y greater than or equal to 3
The y values must be of greater value then 3 meaning 4,5,6, etc. We shaed above the horizontal lines.
y less than or equal to x
This is the diagonal line through (0,0). We shade value for which y is a smaller number then x like (9,3) since 3 (y) less then 9 (x). We shade everything below the line.
y less than -1/2 times x +8
We choose a point like (4,4). We plug in and ask ourselves: Is 4 less than -1/2(4)+8? Is 4 less than -2+8? Is 4 less than 6? Yes. So we shade (4,4) and all points on this side of the line.
The shaded areas overlap in the last answer choice.
