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 + 3y 2. nty 3. 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

Exploring Two-Step Equations COURSE 2 LESSON 2-5 Solutions 1. n + 3y 2. nty 3. 3y – t 4 + 3(3) 4 • 2 • 3 3(3) – 2 4 + 9 24 9 – 2 13 7 4. m – 5 5. 2p 6. d + 5 2-5

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 Let = length of rope in inches. Define the variable. 4 • + 8 Write an algebraic expression. 4 + 8 Rewrite 4 • as 4 . b. half the weight of the cheese in ounces, minus one ounce Let c = weight of cheese in ounces. Define the variable. 1 2 • c – 1 Write an algebraic expression. c – 1 Simplify. 1 2 2-5

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

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. 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 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

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

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

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? 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 2-5

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

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 g 6 d = 10 g = 36 k 3 h = 5 k = 33 2-5