Write Equations and Inequalities Warm Up Lesson Presentation Lesson Quiz

Warm-Up 1. Write an expression for the phrase: 4 times the difference of 6 and a number y. ANSWER 4(6 – 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. 50 + 2t, where t is the number of tickets; $68 ANSWER

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

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

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

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 4. 2n + 3 21; 9 > – solution

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

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

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?

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

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

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? ANSWER Each person pays $7.50.

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 p be the average number of points per game. Write an inequality. 18  p > 351

Example 5 STEP 2 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.

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? ANSWER Yes

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

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