Our Lesson Inequalities with Add and Subtract

Confidential2 1)Seven roses less than Kiran 2)Half as many Oranges as last year 3)One more than a number is 845 4)Eleven fewer hours than her sister 5)One-third the population of California Warm Up

Confidential3 Translate verbal phrases in to algebraic expressions Lets review what we have learned in the last lesson 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 Example:

Confidential4 AdditionSubtraction Words used to express Addition/Subtraction Plus Sum More than Increased by Total Minus Difference Less than Less Decreased by

Confidential5 Words used to express Multiplication/Division MultiplicationDivision Times Product Multiplied Of Twice Thrice Divided Quotient

Confidential6 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

Confidential7 USING A VERBAL MODEL PhraseExpression = SentenceEquation SentenceInequality The sum of six and a number is twelve. 6 + x = 12 In this sentence, “is” says that one quantity is equal to one another In this sentence, the words “is less than” indicate an inequality The sum of six and a number is less than twelve. 6 + x < 12 is less than twelve. 6 + x < 12 The sum of six and a number 6 + x Phrase

Confidential8 Inequalities are used in many things like nutrition, budgeting, Personal financing, and academics g < 68 Grams of fat in snacks Grams of fat remaining Total Grams 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. Lets get Started

Confidential9 An inequality is a statement with a symbol of or ≥ between numerical or variable expressions.  Example: x + 7 ≤ 11. x is a variable.  x  x is 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

Confidential10 Inequality Symbols SYMBOL MEANING < less than > greater than ≤ less than or equal to ≥ greater than or equal to

Confidential11 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

Confidential12 Rules to Solve Linear Inequalities Rule No : 1 - Addition If a < b, then a + c < b + c 2 < 5 and c = 5 a + c < b + c < < 10

Confidential13 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

Confidential14 Solve the inequality x – 7 < 8 Step1: Add 7 on both sides x – < Step2: Add the numbers x < 15 Inverse of - 7 is + 7

Confidential15 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 < < 5

Confidential16 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

Confidential17 Word problems in Inequalities PhrasesTranslation is at least ≥ is at most ≤ cannot exceed ≤ must exceed > is between < and < To solve the word problem translate the phrases and solve it

Confidential18 Example Bill is at least 21 years old Sample SentencesEquivalent Form 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

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Confidential21 1)t - 7 < 14 2) r – 5 > 27 3) k - 34 ≤ 10 4) v – 22 ≥ -11 5) y - 3 < -8 Your Turn

Confidential22 6) x + 5 < 14 7) z + 9 > -7 8) 9) c + 19 ≥ ) u + 13 ≥ 25 Your Turn Boston is more than 200 miles away

Confidential23 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?

Confidential24 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.

Confidential25 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.

Confidential26 An inequality is a statement with a symbol of or ≥ between numerical or variable expressions. Example: x + 7 ≤ 11. x is a variable.  x  x is 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 Lets review what we have Learnt today

Confidential27 Inequality Symbols SYMBOL MEANING < less than > greater than ≤ less than or equal to ≥ greater than or equal to

Confidential28 Word problems in Inequalities PhrasesTranslation is at least ≥ is at most ≤ cannot exceed ≤ must exceed > is between < and < To solve the word problem translate the phrases and solve it

Confidential29 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

Confidential30 You did great in your lesson today ! Be sure to practice and keep up the good work