1. Inequalities Regions

2. 05/06/2006©RSH X  3 Draw the boundary line x = 3. Use a solid line because x = 3 is included. x = 3 Every value of x on this side is greater than 3 x  3 Decide which side of the boundary is needed. Shade the side not needed. The clear region is the one needed.

3. 05/06/2006©RSH X < -1 Draw the boundary line x = -1. Use a dashed line because x = -1 is not included. Decide which side of the boundary is needed. Shade the side not needed. The clear region is the one needed. x = -1 Every value of x on this side is less than -1 x < -1

4. 05/06/2006©RSH y  2 Draw the boundary line y = 2. Use a solid line because y = 2 is included. Decide which side of the boundary is needed. Shade the side not needed. The clear region is the one needed. Y = 2 Every value of y on this side is less than 2 y  2

5. 05/06/2006©RSH x < -1 and y  2 Draw the boundary line x = -1 and shade out the unwanted region. Draw the boundary line y = 2 and shade out the unwanted region. The clear region satisfies both inequalities. Y = 2 x < -1 and y  2 x = -1

6. 05/06/2006©RSH y  x Draw the boundary line y = x. Use a solid line because y = x is included. Decide which side of the boundary is needed. Shade the side not needed. The clear region is the one needed. y = x Every value of y on this side is less than x y  x

7. 05/06/2006©RSH y  x and x < 4 and y  -3 Draw the boundary line y = x. Shade out the unwanted region. Repeat for x = 4 and y = -3. The unshaded area represents the region where y  x and x < 4 and y  -3 y = -3 y = xx = 4

8. 05/06/2006©RSH x + y  5 and x  0 and y  -1 Draw the boundary line x + y = 5. Shade out the unwanted region. Repeat for x = 0 and y = -1. The unshaded area represents the region where x+ y  5 and x  0 and y  -1 y = -1 x + y = 5 x = 0

9. 05/06/2006©RSH x + y  4 and x < 4 and y  -3 Draw the boundary line x + y = 4. Shade out the unwanted region. Repeat for x = 4 and y = -3. The unshaded area represents the region where x+ y  4 and x < 4 and y  -3 y = -3 x + y = 4 x = 4

10. 05/06/2006©RSH y + 2x  1 and x < 4 and y  -3 Draw the boundary line y + 2x = 1. Shade out the unwanted region. Repeat for x = 4 and y = -3. The unshaded area represents the region where y+ 2x  1 and x < 4 and y  -3 y = -3 y + 2x = 1 x = 4