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Our Lesson

Our Lesson. Inequalities with Add and Subtract. Warm Up. Seven roses less than Kiran y – 7 Half as many Oranges as last year ½ m One more than a number is 845 b + 1 = 845 Eleven fewer hours than her sister s -11

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Our Lesson

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  1. Our Lesson Inequalities with Add and Subtract

  2. Warm Up • Seven roses less than Kiran y – 7 • Half as many Oranges as last year ½ m • One more than a number is 845 b + 1 = 845 • Eleven fewer hours than her sister s -11 • One-third the population of California p/3 Confidential

  3. Lets review what we have learned in the last lesson Translate verbal phrases in to algebraic expressions Example: He weighs 180 pounds, which is 22 pounds 180 = 2z-22 less than double her weight Five more hits than the Martins h + 5 Three more than 8 times as many trees is 75 trees 8t – 3 = 75 Confidential

  4. Words used to express Addition/Subtraction Addition Subtraction Minus Difference Less than Less Decreased by Plus Sum More than Increased by Total Confidential

  5. Words used to express Multiplication/Division Multiplication Division Times Product Multiplied Of Twice Thrice Divided Quotient Confidential

  6. USING A VERBAL MODEL In Mathematics there is a difference between a phrase and a sentence. Phrases translate into expressions; sentences translate into equations or inequalities Expressions Phrases Equations or Inequalities Sentences Confidential

  7. = The sum of six and a number 6 + x In this sentence, “is” says that one quantity is equal to one another Sentence Equation In this sentence, the words “is less than” indicate an inequality Sentence Inequality The sum of six and a number is less than twelve. 6 + x < 12 6 + x< 12 is less than twelve. USING A VERBAL MODEL Phrase Expression Phrase 6 + x = 12 The sum of six and a number is twelve. Confidential

  8. Lets get Started Inequalities are used in many things like nutrition, budgeting, Personal financing, and academics. Grams of fat in snacks Total Grams Grams of fat remaining 15+8+4+2 + g < 68 That is, 29 + g < 68 The symbol <indicates less than or equal to. It is used in this situation because the total number of grams of fat in daily diet should be no greater than 68. If this were an equation, we would subtract 29 from each side. Confidential

  9. Defining Inequality An inequality is a statement with a symbol of < , ≤, > or ≥ between numerical or variable expressions. • Example: x + 7 ≤ 11. x is a variable. • xis a very common variable that is used in algebra, but you can use any letter (a, b, c, d, ....) to be a variable Confidential

  10. Inequality Symbols Confidential

  11. Procedures that leave the inequality symbol unchanged • Simplify both sides of the inequality by combining like terms and eliminating parenthesis • Add or subtract the same expression on both sides of the inequality • Multiply or divide both sides of the inequality by the same positive expression Confidential

  12. Rule No : 1 - Addition If a < b, then a + c < b + c 2 < 5 and c = 5 a + c < b + c 2 + 5 < 5 + 5 7 < 10 Rules to Solve Linear Inequalities Confidential

  13. ADDING & SUBTRACTING INEQUALITY Steps:- To solve the inequality means isolate a variable x and move the numbers to the other side of the inequality. To move the number perform the reverse operation. Addition is the reverse of Subtraction Subtraction is the reverse of Addition Confidential

  14. Solve the inequality x – 7 < 8 Step1: Add 7 on both sides x – 7 + 7 < 8 + 7 Step2: Add the numbers x < 15 Inverse of -7 is + 7 Confidential

  15. Rules to Solve Linear Inequalities Rule No : 2 - Subtraction If a < b, then a - c < b - c 4 < 7 c = 2 a - c < b - c 4 – 2 < 7 - 2 2 < 5 Confidential

  16. Solve the inequality y + 6 > -11 Step1: Subtract 6 on both sides y + 6 – 6 > -11 – 6 Step2 : Simplify the inequality y > -17 Inverse of + 6 is - 6 Confidential

  17. Word problems in Inequalities To solve the word problem translate the phrases and solve it Confidential

  18. Example Sample Sentences Equivalent Form Bill is at least 21 years old Bill age is  21 At most 5 students dropped the course Students ≤ 5 The film was between 90 and 100 minutes long. 90 < t < 100 Confidential

  19. Your Turn • t - 7 < 14 t < 21 2) r – 5 > 27 r > 32 3) k - 34 ≤ 10 k ≤ 44 4) v – 22 ≥ -11 v ≥ 11 5) y - 3 < -8 y < 11 Confidential

  20. Your Turn 6) x + 5 < 14 x < 9 7) z + 9 > -7 z > -16 8) 9) c + 19 ≥ -13 c ≥ -32 10) u + 13 ≥ 25 u ≥ 12 Boston is more than 200 miles awayD > 200 Confidential

  21. Refreshment Time Break Time Confidential

  22. LETS PLAY A GAME Click Here to Play Confidential

  23. 1) Lucy earned $400 and $550 in interest, the last 2 years. How much interest must she earn this year so that her average earnings over the three year period is more than $600? Let x be the amount she needs to earn. So the average earnings would be 400 + 550 + x 3 The average must be more than $600. So we need to solve the inequality:   600 < 400 + 550 + x 3 Solve the inequality by multiplying both sides by 3, to clear the fraction, and we have 1800 < 400 + 550 + x Solving for x we have 850 < x Lucy needs to make more than $850 this year. Confidential

  24. 2) Chris has scored a 85 and a 89 on her first two math 23 tests.  What must she get on her third test to have at least a total score of 270.  n = 3rd test score (89 + 85 + n )  270 n = 96 Confidential

  25. 3) Kim decides to take up golf.  Her golf club membership will cost $450 for the season she spends $300 on the gear and now she wants to buy golf shoes. Kim has decided not to spend more than $1000 on golf for the season. How much at most can she pay for the shoes. a) Let x = cost of shoes 450 + 300 + x  1000 x  1000 – 750 x  250 Kim can at most spend $250 for the shoes Confidential

  26. Lets review what we have Learnt today An inequality is a statement with a symbol of < , ≤, > or ≥ between numerical or variable expressions. Example: x + 7 ≤ 11. x is a variable. • xis a very common variable that is used in algebra, but you can use any letter (a, b, c, d, ....) to be a variable Defining Inequality Confidential

  27. Inequality Symbols Confidential

  28. ADDING & SUBTRACTING INEQUALITY Steps:- To solve the inequality means isolate a variable x and move the numbers to the other side of the inequality. To move the number perform the reverse operation. Addition is the reverse of Subtraction Subtraction is the reverse of Addition Confidential

  29. Word problems in Inequalities To solve the word problem translate the phrases and solve it Confidential

  30. You did great in your lesson today ! Be sure to practice and keep up the good work Confidential

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