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Essential Question: How do you write equations and inequalities? Before we start… When you compare things, what phrases do you use? For example, if you were to compare the number of boys in class to the number of girls. – Tell your partner. What is the difference between an equation and an inequality? • An equation is a mathematical sentence formed by placing the symbol = between two expressions. • An inequality is a mathematical sentence formed by placing one of the symbols <, ≤, >, or ≥ between two expressions. What is an open sentence? An equation or inequality that contains an algebraic expression. 4x 8 How do you write equations and inequalities? • Look for key words or phrases that indicate an equation or inequality. • Translate to numbers, variables, operations and symbols. Translating to Equations and Inequalities Symbol Meaning = < ≤ > ≥ is equal to is less than is less than or equal to is greater than is greater than or equal to Associated Words is, is the same as is fewer than is at most, is no more than is more than is at least, is no less than Sometimes two inequalities are combined. Translate to equations or inequalities. The difference of twice a number k and 8 is 12. The product of 6 and a number n is at least 24. Translate to equations or inequalities. A number y is no less than 5 and no more than 13. The quotient of a number p and 12 is at least 30. Translate to equations or inequalities. The sum of twice a number r and 3 is 11. A number q is at least 5 and less than 17. The sum of 12 and the quantity 8 times a number k is equal to 48. The product of 9 and the quantity 5 more than a number t is less than 6. What is a solution? A number when substituted for the variable in an open sentence makes the equation or inequality true. Solution of the equation or a solution of the inequality How do you check possible solutions? Substitute the number in for the variable. Simplify. Check if it is true. Check whether 3 is a solution of the equation or inequality. a. 8 2 x 2 c. 2 z 5 12 b. 4 x 5 6 d. 5 3n 20 Check whether 5 is a solution of the equation or inequality. a. 24 3d 9 c. 2 w 7 3 b. 3 x 4 18 d. 4 3 p 19 Check whether the given number is a solution of the equation or inequality. 9 x 4; 5 b 5 15; 7 2n 3 21; 9 Using Mental Math • Some equations are simple enough to solve using mental math. • Think of the equation as a question. • Once you answer the question, check the solution. Mountain Hiking The last time you and 3 friends went to a mountain bike park, you had a coupon for $10 off and paid $17 for 4 tickets. What is the regular price of 4 tickets? If you pay the regular price this time and share it equally, how much does each person pay? Guitar Lessons Sarah enrolled in a guitar class. The enrollment fee was $25. She paid a total of $70 for the enrollment fee and 3 lessons. What is the cost of 3 lessons? How much did each lesson cost? Charity Walk You are taking part in a charity walk, and you have walked 12.5 miles so far. Your goal is to walk 20 miles. How many more miles do you need to walk to meet your goal? Eco-Challenge Eco-Challenge Fiji was a competition that included jungle trekking, ocean swimming, mountain biking, and river kayaking. In 2002, the U.S. team finished second about 6 hours after the winning team from New Zealand. The U.S. team finished in about 173 hours. What was the winning team’s time? Basketball A basketball player scored 351 points last year. If the player plays 18 games this year, will an average of 20 points per game be enough to beat last year’s total? Selling Coffee Mugs Tyler would like to make no less than $610 selling coffee mugs online. If he sells 28 mugs for $22 each, will he achieve his goal? Gymnastics You need to practice a gymnastic routine for at least 25 hours. You have already practiced 8.5 hours. If you practice for another 16.5 hours, will you reach your goal? Compact Discs You buy a storage rack that holds 40 CDs. You have 27 CDs. Write an inequality that describes how many more CDs you can buy and still have no more CDs than the rack can hold. You buy 15 CDs. Will they all still fit? • How do you write equations and inequalities? Ticket Out the Door • Write an equation or inequality on a piece of paper (put your name on it) and place it in the box on your way out… The product of 4 and a number w is at most 51.