5-1 Solving Inequalities by Addition & Subtraction Objectives: Solve linear inequalities by using addition Solve linear inequalities by using subtraction

Solving Inequalities To solve inequalities we apply the same rules as solving equations. Instead of our answer being one number, we will have a set of numbers as our answer.

Example 1: Solve a) 22>m−8 b) 𝑑−14≥−19

Set-Builder Notation Writing a solution as: 𝑥 𝑥≥6 Read: “the set of all numbers x such that x is greater than or equal to 6” Solutions can be graphed on a number line. If the endpoint is NOT included in the graph use an open circle, other wise use a filled-in circle.

Example 2: Solve, write your answer in set-builder notation. a) 𝑥+23<14 b) 𝑝+8≤18

Example 3: Solve and graph the solution set. a) 9𝑛−1<10𝑛 b) 5ℎ≤12+4ℎ

Verbal problems containing phrases like greater than or less than can be solved by using inequalities. The chart shows other phrases that indicate inequalities.

Example 4: Write an inequality to represent each situation and then solve. a) Michelle has $65 to spend at the mall. She bought a sweater for $18 and leggings for $14. If Michelle wants a pair of jeans, how much can she spend? b) Noah wants to buy season tickets to two theme parks. If one season pass costs $54.99 and Noah has $100 to spend on both passes, the second pass must cost no more than what amount?

Practice WS

Homework 5-1 Pages 288-289: 15-19 odd, 27-33 odd, 37, 43

5-2 Solving Inequalities by Multiplication & Division Objectives: Solve linear inequalities by using multiplication. Solve linear inequalities by using division

Example 1: Solve a) 3𝑥>−27 b) 6≤ 2 3 𝑟 c) 2> 𝑎 10

Example 2: Solve (You try…). Be sure to check your answers!!! a) −3𝑥≥24 b) − 2 5 𝑎<4

When multiplying or dividing by a negative number FLIP THE SIGN

Example 3: Solve and graph. a) −8𝑥>72 b) −3≤ 𝑥 −5

Trivia… What state in the Masters golf tournament held in? Georgia What state in the Masters golf tournament held in? 2. What year was PlayStation introduced? 1994 3. What famous female Pop artist is currently a judge on The Voice? Gwen Stefani

Example 3: Solve and graph. c) −15≥3𝑥 d) 𝑥 −7 <11

Practice WS

Homework 5-2 Pages 295-296: 17-23 odd, 31, 33