# Inequalities

18. match the system of inequalities to a region in the picture

x + 2y <= 8

3x - 2y <= 0

22. solve the system of linear inequalities graphically

3x + 4y <= 12

y >= -3

32. solve the system of linear inequalities graphically, find the coordinates of each corner points, and indicate whether the solution region is bounded or unbounded

3x + 4y <= 24

x >= 0

y >= 0

38. solve the system of linear inequalities graphically, find the coordinates of each corner points, and indicate whether the solution region is bounded or unbounded

3x + y <=21

x + y <= 9

x >= 0

y >= 0

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#### Solution Preview

18. match the system of inequalities to a region in the picture

x + 2y <= 8

3x - 2y <= 0

In this question, and in all the other ones, I'm first going to put the inequalities in slope-intercept format. In the second inequality, notice that you have to switch the direction of the sign when dividing both sides by -2.

x + 2y <= 8 3x - 2y <= 0

2y <= -x + 8 -2y <= -3x

y <= (-1/2)x + 4 y >= (3/2)x

For the first inequality, you'd shade below the line with a slope of -1/2 and a y-intercept of 4. For the second inequality, you'd shade below the line with a slope of 3/2 and a y-intercept of 0.

The region that satisfies both these conditions is region ...

Step-wise answer to Inequalities

1. Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not?

Write an inequality to be solved with the answer. In your inequality, use both the multiplication and addition properties of inequalities.

2. How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.

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