Write equations and inequalities EXAMPLE 1 a. The difference of twice a number k and 8 is 12. b. The product of 6 and a number n is at least 24. 6n ≥ 24.

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Write equations and inequalities EXAMPLE 1 a. The difference of twice a number k and 8 is 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. Verbal SentenceEquation or Inequality 5 ≤ y ≤ 13 2k – 8 = 12

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

EXAMPLE 3 Use mental math to solve an equation Equation a. x + 4 = 10 b. 20 – y = 8 c. 6n = 42 a 5 =9 d.d. Think What number plus 4 equals 10? 20 minus what number equals 8? 6 times what number equals 42? What number divided by 5 equals 9? Solution Check = –12 = 8 6(7) = =9

GUIDED PRACTICE for Examples 2 and 3 Check whether the given number is a solution of the equation or inequality – x = 4; 5 3. b + 5 < 15; n ; 9 > – solution

GUIDED PRACTICE for Examples 2 and 3 Solve the equation using mental math. 5. m + 6 = x = r =

Solve a multi-step problem EXAMPLE 4 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 ? Mountain Biking

Solve a multi-step problem EXAMPLE 4 Write a verbal model. Let p be the regular price of 4 tickets. Write an equation. SOLUTION STEP 1 p – 10 = 17 Regular price Amount of coupon  Amount paid =

Solve a multi-step problem EXAMPLE 4 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. ANSWER Each person pays $6.75. = $6.75 per person.Find the cost per person: $27 4 people STEP 2 STEP 3

SOLUTION Write and check a solution of an inequality EXAMPLE 5 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 ? Write a verbal model. Let p be the average number of points per game. Write an inequality. Basketball STEP 1 18 p > 351 Number of games Points per game Total points last year =

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

GUIDED PRACTICE for Examples 4 and 5 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.

GUIDED PRACTICE for Examples 4 and 5 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