3-1 Inequalities and Their Graphs

Quick Review

A solution of an inequality is any number that makes the inequality true. You can indicate all the solutions of an inequality on the graph. A closed dot indicates that the endpoint is a solution. An open dot indicates that the endpoint is not a solution.

Example

What is the graph of x ≤ − 4 ? bold x less than or equal to negative 4 question mark

Exercises

Graph each inequality.

6. x > 5 x greater than 5
7. h ≤ − 1 h less than or equal to negative 1
8. 10 ≥ p 10 greater than or equal to p
9. r < 3.2 r less than 3.2

Write an inequality for each graph.

3-2 Solving Inequalities Using Addition or Subtraction

Quick Review

You can use the addition and subtraction properties of inequality to transform an inequality into a simpler, equivalent inequality.

Example

What are the solutions of x + 4 ≤ 5 ? bold x plus 4 less than or equal to 5 question mark

x + 4 ≤ 5   x + 4 − 4 ≤ 5 − 4 Subtract  4  from each side  . x ≤ 1  Simplify. table with 3 rows and 3 columns , row1 column 1 , x plus 4 , column 2 less than or equal to 5 , column 3 , row2 column 1 , x plus 4 minus 4 , column 2 less than or equal to 5 minus 4 , column 3 cap subtract . 4 . fromeachside . . , row3 column 1 , x , column 2 less than or equal to 1 , column 3 cap simplify. , end table

Exercises

Solve each inequality. Graph your solutions.

13. w + 3 > 9 w plus 3 greater than 9
14. v − 6 < 4 v minus 6 less than 4
15. − 4 < t + 8 negative 4 less than t plus 8
16. n − 1 2 ≥ 3 4 n minus , 1 half , greater than or equal to , 3 fourths
17. 22.3 ≤ 13.7 + h 22.3 , less than or equal to , 13.7 , plus h
18. q + 0.5 > − 2 q plus 0.5 greater than negative 2
19. Allowance You have at most $15.00 to spend. You want to buy a used CD that costs $4.25. Write and solve an inequality to find the possible additional amounts you can spend.

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