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Write equations and inequalities

EXAMPLE 1. Write equations and inequalities. Verbal Sentence. Equation or Inequality. a . The difference of twice a number k and 8 is 12. 2 k – 8 = 12. b . The product of 6 and a number n is at least 24. 6 n ≥ 24. 5 ≤ y ≤ 13.

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Write equations and inequalities

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  1. EXAMPLE 1 Write equations and inequalities 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.

  2. ANSWER P 30 12 > – for Example 1 GUIDED PRACTICE 1.Write an equation or an inequality: The quotient of a number pand 12 is at least30.

  3. ? 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 possible solutions 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

  4. 6 + 4 = 10 20 –12 = 8 6(7) = 42 45 = 9 5 a d. = 9 5 EXAMPLE 3 Use mental math to solve an equation 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

  5. > – 4.2n + 3 21; 9 for Examples 2 and 3 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

  6. 7. r = 10 4 for Examples 2 and 3 GUIDED PRACTICE Solve the equation using mental math. 5 5. m + 6 = 11 8 6. 5x = 40 40

  7. EXAMPLE 4 Solve a multi-step problem 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?

  8. Regularprice  Amountpaid Amountof coupon = EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 Write a verbal model. Let pbe the regular price of 4 tickets. Write an equation. p – 10 = 17

  9. ANSWER The regular price for 4 tickets is $27. $27 4 people ANSWER Each person pays $6.75. EXAMPLE 4 Solve a multi-step problem 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.

  10. Numberof games • Total pointslast year Points pergame = 18 p > 351 EXAMPLE 5 Write and check a solution of an inequality 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.

  11. 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 Write and check a solution of an inequality STEP 2

  12. ANSWER Each person pays $7.50. for Examples 4 and 5 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. ANSWER Yes for Examples 4 and 5 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?

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