1. Unit 1 – First-Degree Equations and Inequalities
Chapter 1 – equations and inequalities
1.5 – Solving Inequalities

2. 1.5 – Solving Inequalities
In this section we will review:
Solving inequalities with one operation
Solving multi-step inequalities

3. 1.5 – Solving Inequalities
Trichotomy Property – For any two real numbers a and b, exactly one of the following statements in true:
a < b
a = b
a > b

4. 1.5 – Solving Inequalities
Addition Property of Inequality
For any real numbers a, b and c:
If a > b, then a + c > b + c
If a < b, then a + c < b + c
Example
3 < 5
3 + (-4) < 5 + (-4)
-1 < 1

5. 1.5 – Solving Inequalities
Subtraction Property of Inequality
For any real numbers a, b and c:
If a > b, then a – c > b – c
If a < b, then a – c < b – c
Example
2 > -7
2 – 8 > -7 – 8
-6 > -15

6. 1.5 – Solving Inequalities
Example 1
Solve 4y – 3 < 5y Graph the solution set on a number line.

7. 1.5 – Solving Inequalities
REMEMBER:
When multiplying or dividing each side by a NEGATIVE number, you must reverse the inequality symbol

8. 1.5 – Solving Inequalities
Multiplication Property of Inequality
For any real numbers a, b and c where c is positive:
If a > b, then ac > bc
If a < b, then ac < bc
Example
-2 < 3
4(-2)< 4(3)
-8 < 12

9. 1.5 – Solving Inequalities
Division Property of Inequality
For any real numbers a, b and c where c is negative:
If a > b, then ac < bc
If a < b, then ac > bc
Example
5 > -1
(-3)5 > (-3)(21)
-15 < 3

10. 1.5 – Solving Inequalities
Division Property of Inequality
For any real numbers a, b and c where c is positive:
If a > b, then a/c > b/c
If a < b, then a/c < b/c
Example
-18 < -9
-18/3< -9/3
-6 < -3

11. 1.5 – Solving Inequalities
Division Property of Inequality
For any real numbers a, b and c where c is negative:
If a > b, then a/c < b/c
If a < b, then a/c > b/c
Example
12 > 8
12/-2 > 8/-2
-6 < -4

12. 1.5 – Solving Inequalities
The solution set of an inequality can be expressed by using set-builder notation
{x | x > 9}
The set {} of all numbers x such that (|) x is greater than (>) 9

13. 1.5 – Solving Inequalities
Example 2
Solve 12 ≥ -0.3p. Graph the solution set on a number line.

14. 1.5 – Solving Inequalities
Example 3
Solve –x > (x – 7)/2. Graph the solution set on a number line.

15. 1.5 – Solving Inequalities
Example 4
Alida has at most $15.00 to spend today. She buys a bag of potato chips and a can of soda for $ If gasoline at this store costs $2.89 per gallon, how many gallons of gasoline, to the nearest tenth of a gallon, can Alida buy for her car?

16. 1.5 – Solving Inequalities
HOMEWORK Page 37 #11 – 43 odd, 45 – 51 all