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Algebra I

Algebra I. 1.4 Write Equations And Inequalities. VOCAB Equation – a mathematical sentence formed by placing the symbol = between two expressions Inequality – a mathematical sentence formed by placing one of the symbols <, >, ≤, or ≥ between two expressions. VOCAB

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Algebra I

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  1. Algebra I 1.4 Write Equations And Inequalities

  2. VOCAB Equation– a mathematical sentence formed by placing the symbol = between two expressions Inequality – a mathematical sentence formed by placing one of the symbols <, >, ≤, or ≥ between two expressions

  3. VOCAB Open Sentence– an equation or inequality that contains an algebraic expression Solution to an Equation –a number that makes the sentence true Solution to an Inequality – a number or set of numbers that makes the sentence true

  4. 1.4 Write Equations and Inequalities

  5. 1.4 Write Equations and Inequalities The BIG Difference Equations: Have ONLY ONE Solution! Inequalities: Have MANY Solutions!!!!!

  6. 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

  7. ANSWER P 30 12 > – for Example 1 GUIDED PRACTICE c. A number yis no less than 5 and nomore than13. 5 ≤ y ≤ 13 d. Write an equation or an inequality: The quotient of a number pand 12 is at least30.

  8. ? 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

  9. 4 = 4 5 is a solution. 9 – 5 4 > – > >  – – 10<15 5is a solution. ? c.2n + 3 21 5 + 5 15 < 2(5) + 3 21 13 215 is NOT a solution. ? ? = for Example 2 GUIDED PRACTICE Check to see whether or not 5 is a solution of the equation or inequality. Substitute Equation/Inequality Conclusion a.9 – x = 4 b.b + 5 < 15 X

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

  11. 7. r = 10 40 = 10  4 4 for Example 3 GUIDED PRACTICE Solve the equation using mental math. Equation Solution Check Think 5. m + 6= 11 5 5 + 6 = 11  What number plus 6 equals11? 5(8) = 40  5times whatnumber equals40? 6. 5x = 40 8 What number dividedby 4 equals 10 40

  12. Answer Now Is 2 a solution to 4z – 5 < 3? • A solution • NOT a solution

  13. Answer Now Solve for f: • 0 • 12 • 24 • 4

  14. 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?

  15. EXAMPLE 4 Solve a multi-step problem Step 1: Write a verbal model. Let p be the regular price of 4 tickets. Write an equation. Regular Price – Coupon = Amount Paid P – 10 = 17

  16. 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 is 17? • Because 27 – 10 = 17, the solution is 27. • Answer: The regular price for 4 tickets is $27. • Step 3: Find Cost Per Person • $27 / 4 people = 6.75 • Answer: $6.75 per person.

  17. for Examples 4 and 5 GUIDED PRACTICE WHAT IF? 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?

  18. for Examples 4 and 5 GUIDED PRACTICE STEP 1: Write a verbal model. Let p be the regular price of 4 tickets. Write an equation. Regular Price – Coupon = Amount Paid r – 15 = 15

  19. for Examples 4 and 5 GUIDED PRACTICE STEP 2: Use mental math to solve the equation p – 15=15. Think: 15 less than what number is 15? Because 30 – 15 = 15, the solution is 30. So the full price is $30. STEP 3: Find the Cost Per Person $30/4 = 7.5 Answer: $7.50 per person

  20. EXAMPLE 5 Write and check a solution of an inequality STEP 1: Write a verbal model. Let p be the average number of points per game. Write an inequality. Number of Games • Number of Points Per Game > Total Points Last Year 18 • p > 351 STEP 2: Check that 20 is a solution of the in equality18p > 351. 18(20) = 360 360 > 351 Answer: An average of 20 points per game will be enough.

  21. for Examples 4 and 5 GUIDED PRACTICE WHAT IFSuppose that the player plays 16 games. Would an average of 22 points per game be enough to beat last year’s total? STEP 1:Write a verbal model. Let p be the average number of points per game. Write an inequality. Number of Games • Number of Points Per Game = Total Points Last Year STEP 2:Check that 22 is a solution of the in equality16p > 351. Because 16(22) = 352 352 > 351 So, 22 is a solution.

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