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

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

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

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

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

1.5 – Solving Inequalities Example 1 Solve 4y – 3 < 5y + 2. Graph the solution set on a number line.

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

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

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

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

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

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

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

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

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 $1.59. 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?

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