Solving Two-Step Equations-PPT part 1
- 1. Chapter 3 Section 1 Solving Two-Step Equations Miss Emily Howard Central Michigan University Technology in Education
- 2. Today’s Lesson • Solving two-step equations
- 3. But first…Checkpoint Review • Solve for x x + 3 = 37 (Prentice Hall 2005)
- 4. Checkpoint Review Continued • Solve for x x + 3 = 37 -3 -3 Subtract 3 x = 34 Answer (Prentice Hall 2005)
- 5. Taking it a step further… • Example 1 Solve for x. x - 8 = 12 2 (Prentice Hall 2005)
- 6. Solving Two-Step Equations • Example 1 Solve for x. x - 8 = 12 2 + 8 +8 Step 1: Add 8 x = 20 Simplify 2 (2) x = 20 (2) Step 2: Multiply by 2 2 x = 40 Answer (Prentice Hall 2005)
- 7. Solving Two-Step Equations • Example 2 Solve for m. 21 = -m + 7 (Prentice Hall 2005)
- 8. Solving Two-Step Equations • Example 2 Solve for m. 21 = -m + 7 -7 -7 Step 1: Subtract 7 14 = -m Simplify 14 ÷ (-1) = -m ÷ (- 1) Step 2: Divide by (-1) -14 = m Answer (Prentice Hall 2005)
- 9. Solving Two-Step Equations • Example 3: Real World Problem Solving • A music store sells a copy of a deluxe electric guitar for $295. This is $30 more than one-third the cost of the deluxe electric guitar it is modeled after. What is the cost of the deluxe electric guitar? (Prentice Hall 2005)
- 10. Solving Two-Step Equations • Example 3: Real World Problem Solving • A music store sells a copy of a deluxe electric guitar for $295. This is $30 more than one-third the cost of the deluxe electric guitar it is modeled after. What is the cost of the deluxe electric guitar? the cost of the cost of 1 Relate: the copy is $30 more than deluxe electric 3 guitar Define: Let c = the cost of the deluxe electric guitar 1 Write: 295 = 30 + 3 c (Prentice Hall 2005)
- 11. Solving Two-Step Equations • Example 3: Real World Problem Solving 1 295 = 30 + c Solve for c 3 - 30 -30 Step 1: Subtract 30 1 265 = c Simplify 3 1 (3)265 = c (3) Step 2: Multiply by the 3 3 reciprocal, 3 ( 1 ) 795 = c Answer (Prentice Hall 2005)
- 12. Solving Two-Step Equations • Example 3: Real World Problem Solving c = 795 Answer the cost of the cost of 1 the copy is $30 more than 3 deluxe electric guitar 1 $295 is $30 more than 3 $795 1 295 = 30 + 3 (795) 295 = 30 + 265 295 = 295 (Prentice Hall 2005)
- 13. Solving Two-Step Equations • Example 3: Writing a Function • In a catalog, tulips cost $0.75 each and shipping costs are $3.00. • Write a rule that describes the amount spent as a function of the number of the bulbs ordered. • Then, determine the greatest number of bulbs you can order for $14. (Prentice Hall 2005)
- 14. Solving Two-Step Equations • Example 3: Writing a Function • Ina catalog, tulips cost $0.75 each and shipping costs are $3.00. • Write a rule that describes the amount spent as a function of the number of the bulbs ordered. • Then, determine the greatest number of bulbs you can order for $14. number amount cost per Relate: spent equals tulip bulb times of tulip plus shipping bulbs Define: Let a = amount spent Let b = number of bulbs you can order Write: a = 0.75 × b + 3 This is our function (Prentice Hall 2005)
- 15. Solving Two-Step Equations • Example 3: Writing a Function Part 1 of the problem was to write a function for this story problem. a = 0.75 b + 3 Part 2 asks us to figure out the greatest number of bulbs we can order for $14. $14 is our total cost or amount spent, so we can plug that value in for (a). a = 14 14 = 0.75 b + 3 Solve for b -3 -3 Step 1: Subtract 3 11 = 0.75b Simplify 11 ÷ 0.75 = 0.75b ÷ 0.75 Step 2: Divide by 0.75 14.667 = b Simplify Answer: b = 14 (Prentice Hall 2005)
- 16. Solving Two-Step Equations • Questions? • Thank you! • Homework: • Ch. 3 Section 1 p. 122 • #1-20 multiples of 3, 21-23, 28-39 • Due Tuesday (Prentice Hall 2005)
- 17. Works Cited Prentice Hall. (2005). Prentice Hall Mathematics: Algebra 1 Student Edition. Upper Saddle River, NJ: Prentice Hall.