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Section 1-5 Solving Inequalities 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 : ≠ Less than < Not equal 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. Example: Solving and graphing an inequality Ex) Graph the solution on a number line. 3(2 x 5) 1 4 6 x 15 1 4 6 x 16 4 16 16 6 x 12 6 6 x2 0 2 Closed circle when ≥ or ≤ Solving and graphing multi-step inequalities video. (1 ex, 1 practice) Compound inequalities: two inequalities joined together with the word “and” or “or” AND inequality 5 2 x 1 and 2 x 1 13 5 2 x 1 13 1 1 1 4 2 x 12 2 2 2 2 x6 x 2 and x 6 Writing and solving compound inequality “AND” video real world fitness word problem x≤6 x>2 0 2 AND means that a solution makes BOTH inequalities true. Where the lines overlap 6 OR inequality 7 k 6 OR 8 k 3 7k 6 -7 -7 k 1 -5 OPEN circle when <,> OR 8 k 3 OR 8 8 k 5 -1 0 Writing and solving a compound inequality containing OR video. 2 ex) 1 word problem ALWAYS, NEVER, SOMETIMES? If the statement is always true, ALL real numbers are solutions If the statement is false, then the inequality has no solution Inequalities with no solution or all real numbers as solutions video. 1 ex) 1 practice, party budget x 4 or x 5 -5 0 4 x 4 and x 5 -4 0 5 Practice Standard Pg. 38 #11-43 odd, 44-61 Honors Pg 38. #11-43 odd, 44-66 Standardized test prep: 67-70 ANSWERS in back of book Lesson quiz 1-5 1. What inequality represents the sentence, “The product of: 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 per month, and no initial fee. After how many months of use would Eastside cost less than Valley? 4. Is the inequality sometimes, always, or never true? 3(4x + 2) + x ≤ 1 + 13x 5. What is the solution of 2 ≤ 3x + 8 and 20 > 4x? Graph the solution. Quiz answers 6