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Exploring Two-Step Equations

Exploring Two-Step Equations. COURSE 2 LESSON 2-5. (For help, go to Lesson 2-1.). Evaluate each expression for n = 4, t = 2, and y = 3. 1. n + 3 y 2. nty 3. 3 y – t Write an algebraic expression for each word phrase. 4. 5 minutes fewer than m minutes

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Exploring Two-Step Equations

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  1. Exploring Two-Step Equations COURSE 2 LESSON 2-5 (For help, go to Lesson 2-1.) Evaluate each expression for n = 4, t = 2, and y = 3. 1.n + 3y2.nty3. 3y – t Write an algebraic expression for each word phrase. 4. 5 minutes fewer than m minutes 5. 2 times the number of points p 6. $5 more than d dollars 2-5

  2. Exploring Two-Step Equations COURSE 2 LESSON 2-5 Solutions 1.n + 3y2.nty3. 3y – t 4 + 3(3) 4 • 2 • 3 3(3) – 2 4 + 9 24 9 – 2 13 7 4.m – 5 5. 2p6.d + 5 2-5

  3. Let = length of rope in inches.Define the variable. 4 • + 8Write an algebraic expression. 4 + 8 Rewrite 4 • as 4 . Let c = weight of cheese in ounces.Define the variable. • c – 1 Write an algebraic expression. 1 2 c – 1 Simplify. 1 2 Exploring Two-Step Equations COURSE 2 LESSON 2-5 Define a variable and write an algebraic expression for each phrase. a. four times the length of a rope in inches, increased by eight inches b. half the weight of the cheese in ounces, minus one ounce 2-5

  4. Let m = the number of marbles.Define the variable. 1 4 • m – 6Write an algebraic expression. Note that the order is different from the order in the word phrase. m – 6 Simplify. 1 4 Exploring Two-Step Equations COURSE 2 LESSON 2-5 (continued) c. six fewer than one fourth of the marbles 2-5

  5. Words cost per times number of plus basic • hour hours fee • Let h = number of hours rented. Let C = total cost • Expression 2 • h + 12 Exploring Two-Step Equations COURSE 2 LESSON 2-5 To rent a bicycle, you pay a $12 basic fee plus $2 per hour. Write an equation for the total cost in dollars of a bicycle rental. • Now set the expression equal to the total cost to make an equation. • Equation 2h + 12 = C • Multiplying the hours rented by 2 and adding the basic fee = the total cost. 2-5

  6. – 4 = 14Cover 9k. Think: What number minus 4 is 14? Answer: 18 9k = 18So , or 9k, must equal 18. 9 • = 18 Think: What number times 9 is 18? Answer: 2 k = 2 So , or k, must equal 2. Exploring Two-Step Equations COURSE 2 LESSON 2-5 Solve 9k – 4 = 14 using number sense. 9k – 4 = 14 2-5

  7. Check 9k – 4 = 14 Check your solution in the original equation. 9(2) – 4 14Substitute 2 for k. 18 – 4 14 Simplify. 14 = 14 The solution checks. Exploring Two-Step Equations COURSE 2 LESSON 2-5 (continued) 2-5

  8. Words amount plus (amount to is $200 • already save per • saved month • 6) • Let z = amount to save per month. • Equation 80 + (z • 6) = 200 Exploring Two-Step Equations COURSE 2 LESSON 2-5 The Healy family wants to buy a DVD player that costs $200. They already have $80 saved toward the cost. How much will they have to save per month for the next six months in order to have the whole cost saved? 2-5

  9. 80 + = 200 Cover 6z. Think: What number added to 80 is 200? Answer: 120. • 6z = 120So , or 6z, must equal 120. • 6 = 120 Think: What number times 6 is 120? Answer: 20. • z = 20 So , or z, must equal 20. Exploring Two-Step Equations COURSE 2 LESSON 2-5 (continued) • 80 + 6z = 200 • They will have to save $20 per month. 2-5

  10. g 6 k 3 Exploring Two-Step Equations COURSE 2 LESSON 2-5 Solve each equation using number sense. 1. 5d + 3 = 53 2. – 4 = 2 3. 7h – 10 = 25 4. + 20 = 31 d = 10 g = 36 h =5 k =33 2-5

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