2 In this lesson you will solve and graph inequalities; and write and solve compound inequalities. An Inequality is a relation between two expressions that are not equal. Using signs like :Not equal ≠Less than <Greater than >Less than or equal to ≤Greater than or equal to ≥The solution of an inequality is the numbers that make it true. The solution can be a range of numbers and When solving inequalities you use the same method for solving equations. However, when you multiply or divide by a negative number the inequality sign flips.
3 Example: Solving and graphing an inequality Graph the solution on a number line.2Closed circle when≥ or ≤Solving and graphing multi-step inequalities video. (1 ex, 1 practice)
4 Compound inequalities: two inequalities joined together with the word “and” or “or” AND inequalityWriting and solving compound inequality “AND” video real world fitness word problemx ≤ 6x > 226AND means that a solution makes BOTH inequalities true. Where the lines overlap
5 OPEN circle when < , > OR inequalityWriting and solving a compound inequality containing OR video. 2 ex) 1 word problem-5-1OPEN circle when < , >
6 ALWAYS, NEVER, SOMETIMES? If the statement is false, then the inequality has no solutionIf the statement is always true, ALL real numbers are solutionsInequalities with no solution or all real numbers as solutions video. 1 ex) 1 practice, party budget4-5-45ALWAYSAll real #’sNEVERNo solution
7 Practice Standard Pg. 38 #11-43 odd, 44-61 Honors Pg 38. #11-43 odd, 44-66Standardized test prep: 67-70
9 Lesson quiz 1-5 Quiz answers Lesson Quiz 1. 6x , 20 2. x $ 1 1. What inequality represents the sentence, “The product of: 6 and a number is less than 20”?2. What is the solution of -5(2x - 1) + 3 ≤ -2?Graph the solution.3. Do you UNDERSTAND? Eastside Gym charges a $60 initial fee and $28.50 per month. Valley Gym charges $36 permonth, and no initial fee. After how many months of usewould Eastside cost less than Valley?4. Is the inequality sometimes, always, or never true?3(4x + 2) + x ≤ x5. What is the solution of 2 ≤ 3x + 8 and 20 > 4x?Quiz answersLesson Quiz1. 6x , 202. x $ 13 2 3. More than 8 months.4. never true5. 22 # x , 53 2