Chapter 1: Expressions, Equations, and Inequalities Section 1.5: Solving Inequalities

Section 1.5: Solving Inequalities Goal: To solve and graph inequalities and to write and solve compound inequalities

Section 1.5: Solving Inequalities Inequality: a comparison of two mathematical expressions Symbols: < is less than is less than or equal to > is greater than is greater than or equal to Solutions are any number(s) that make the inequality true Solving inequalities is similar to solving equations except that when dividing or multiplying by a negative, the inequality sign must be flipped

Section 1.5: Solving Inequalities Examples: What inequality represents the sentence, “The product of 7 and a number is no more than 50”? Solve and graph the solution for: 4 (x – 7) > -20

Section 1.5: Solving Inequalities Examples: Plumber A charges $75 for a service charge and $40 per hour. Plumber B charges $50 per hour but no service charge. How many hours must a plumbing job last for Plumber A to cost less than Plumber B?

Section 1.5: Solving Inequalities Examples: Is the inequality sometimes, always, or never true? 3 (x + 3) ≥ 3 (2 + x) 9 – x – 5 < -x + 4

Section 1.5: Solving Inequalities Compound Inequality: two inequalities joined by the word and or the word or Solutions for a compound inequality involving the word and must be a solution for both inequalities (the common area or overlap) Solutions for a compound inequality involving the word or can be a solution to one inequality or the other (include both graphs)

Section 1.5: Solving Inequalities Examples: 5. What is the solution of and -3a + 5 < 8 ? Graph the solution.

Section 1.5: Solving Inequalities Examples: What is the solution of 5 – 2m ≥ 21 or 4m – 1 ≥ -21 ? Graph the solution.

Section 1.5: Solving Inequalities Homework: Pg. 38 #10 – 50 (even)