Adapted version of power point. Not all answers are given in power point so use this power point to refresh your skills.

2. Graph an Inequality in One Variable Write a verbal phrase to describe the inequality. Then graph the inequality. 1. x < 2 INEQUALITY VERBAL PHRASE GRAPH 3. x  1 All real numbers greater than -2 -3 -2 -1 0 1 2 3 2. 4. EXAMPLE 1

4. A solution of an inequality in one variable is a value of the variable that makes the inequality true. Equivalent inequalities have the same solutions. EXAMPLE: x  5 and 5  x are equivalent inequalities.

5. PROPERTIES OF INEQUALITY Addition Property of Inequality For all real numbers a , b, and c : If a > b , then a + c > b + c If a < b , then a + c < b + c Subtraction Property of Inequality For all real numbers a , b, and c : If a > b , then a - c > b - c If a < b , then a - c < b - c

6. Use Subtraction to Solve an Inequality Solve x + 5  3. Then graph the solution. EXAMPLE 2

8. Use Addition to Solve an Inequality Solve -2 > n – 4. Then graph the solution. EXAMPLE 3

10. Write an Inequality with One Variable. Real-World Connection: Page 105: Nearly 32 megabytes (MB) of memory are available for running your computer. If its basic system requires 12.1 MB, how much memory is available for other programs? Memory for basic system PLUS Memory for other programs IS LESS THAN Total memory We don’t know m = memory available for other programs. 21.1 + m < 32 12.1 + m < 32 -12.1 -12.1 m < 19.9 There is LESS THAN 19.9 MB of memory available for other programs. EXAMPLE 4

12. Multiply by a Positive Number EXAMPLE 1 Solve . Then graph the solution.

13. Divide by a Positive Number Solve: 4 x > 20 Then graph the solution. EXAMPLE 2

15. PROPERTIES OF INEQUALITY Multiplication Property of Inequality ( c < 0) For all real numbers a , b, and for c < 0: If a > b , then ac < bc If a < b , then ac > bc Division Property of Inequality ( c < 0) For all real numbers a , b, and c < 0: If a > b , then a ÷ c < b ÷ c If a < b , then a ÷ c > b ÷ c

17. Example of Inequalities Flipping 36  -9t -9 ÷ 36  -9t ÷ -9 -4  t If you get confused by flipping the inequality, instead, you can just flip the sides the numbers are on and keep the inequality the same. t/ -3 < 7 (-3)t/ -3 < 7(-3) t > -21

18. Multiply by a Negative Number EXAMPLE 3 Solve . Then graph the solution.

19. Divide by a Negative Number EXAMPLE 4 Solve . Then graph the solution.

20. Solve the inequality. Then graph the solution Checkpoint Multiply or Divide by a Negative Number.

22. Assignment #13: Pages 106-107: 9-21 odd (just solve, don’t graph), 28, 31. Pages 111-112: 13-27 all.