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Equations and Inequalities Warm-Up Lesson

This lesson covers writing equations and inequalities, solving them, and checking solutions. It also includes practice problems and a quiz.

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Equations and Inequalities Warm-Up Lesson

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  1. Write Equations and Inequalities Warm Up Lesson Presentation Lesson Quiz

  2. ANSWER 4(6 – y) ANSWER 50 + 2t, where t is the number of tickets; $68 Warm-Up 1. Write an expression for the phrase: 4 times the difference of 6 and a number y. 2. A museum charges $50 for an annual membership and then a reduced price of $2 per ticket. Write an expression to represent the situation. Then find the total cost to join the museum and buy 9 tickets.

  3. Example 1 Verbal Sentence Equation or Inequality a. The difference of twice a numberk and8is 12. 2k – 8 = 12 b. The product of 6 and a number n is at least24. 6n ≥ 24 5 ≤ y ≤ 13 c. A number yis no less than 5 and nomore than13.

  4. ANSWER p 30 12 > – Guided Practice 1.Write an equation or an inequality: The quotient of a number pand 12 is at least30.

  5. ? 8 – 2(3) 2 ≤ 2 = 2 3 is a solution. 4(3) – 5 6 7 = 6 3is not a solution. X 2(3) + 5 12 11 > 12 3 is not a solution. X 5 + 3(3) 20 ? ? ? > = = 14 ≤ 203is a solution. Example 2 Check whether 3 is a solution of the equation or inequality. Substitute Equation/Inequality Conclusion a.8 – 2x = 2 b.4x– 5=6 c.2z + 5 > 12 d.5 + 3n ≤ 20

  6. > – 4.2n + 3 21; 9 Guided Practice Check whether the given number is a solution of the equation or inequality. 2.9 – x = 4; 5 solution 3.b + 5< 15; 7 solution solution

  7. 6 + 4 = 10 20 –12 = 8 6(7) = 42 45 = 9 5 a d. = 9 5 Example 3 Equation Solution Check Think a. x + 4 = 10 6 What number plus 4 equals10? 20minus whatnumber equals8? b. 20 –y = 8 12 c. 6n = 42 6times what numberequals42? 7 What number divided by 5 equals 9? 45

  8. 7. r = 10 4 Guided Practice Solve the equation using mental math. 5 5. m + 6 = 11 8 6. 5x = 40 40

  9. Example 4 Mountain Biking 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?

  10. Example 4 SOLUTION STEP 1 Write a verbal model. Let pbe the regular price of 4 tickets. Write an equation. = p 10 17 

  11. ANSWER The regular price for 4 tickets is $27. $27 4 people ANSWER Each person pays $6.75. Example 4 STEP 2 Use mental math to solve the equation p – 10 = 17.Think:10 less than what number is17?Because 27 – 10 = 17, the solution is 27. STEP 3 Find the cost per person: = $6.75 per person.

  12. ANSWER Each person pays $7.50. Guided Practice WHAT IF? In Example 4, suppose that the price of 4 tickets with a half-off coupon is $15. What is each person’s share if you pay full price?

  13. Example 5 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? STEP 1 SOLUTION Write a verbal model. Let pbe the average number of points per game. Write an inequality. p > 18  351

  14. Check that 20 is a solution of the inequality 18p > 351. Because 18(20) = 360 and 360 > 351, 20 is a solution. ANSWER An average of 20 points per game will be enough. Example 5 STEP 2

  15. ANSWER Yes Guided Practice WHAT IF?In Example 5, suppose that the player plays 16 games. Would an average of 22 points per game be enough to beat last year’s total?

  16. 8 8; 2is not a solution. ANSWER 2n – 3 = 12 ANSWER 5k 30 ANSWER < – > / Lesson Quiz Write an equation or an inequality. 1. 3less than twice a number n is12. 2. The product of 5 and a number k is no more than 30. • Check whether 2 is a solution of the inequality • 3p + 2 > 8 3.

  17. 4. • 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? Explain. Yes; the inequality h + 8.5 25 represents the situation. If you substitute 16.5 for h, 16.5 + 8.5 = 25 and2525. ANSWER > > – – Lesson Quiz

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