1. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Also covered: AF1.1 California Standards

2. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Two-step equations contain two operations. For example, the equation 6x  2 = 10 contains multiplication and subtraction. 6x  2 = 10 Subtraction Multiplication

3. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Translate the sentence into an equation. Twice a number m increased by –4 is 0. Translating Sentences into Two-Step Equations Twice a number m increased by –4 is 0. 2 ● m + (–4) = 0 2m + (–4) = 0

4. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Translate the sentence into an equation. 7 more than the product of 3 and a number t is 21. 7 more than the product of 3 and a number t is 16. 3 ● t + 7 = 16 3t + 7 = 16

5. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Solve 3x + 4 = –11. Solving Two-Step Equations Using Division 3x + 4 = –11Step 1: Note that x is multiplied by 3. Then 4 is added. Work backward: Since 4 is added to 3x, subtract 4 from both sides. – 4 3x = –15 Step 2: 3x = –15 3 3 x = –5 Since x is multiplied by 3, divide both sides by 3 to undo the multiplication.

6. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Solve 8 = –5y – 2. Solving Two-Step Equations Using Division 8 = –5y – 2 Since 2 is subtracted from –5y, add 2 to both sides to undo the subtraction. + 2 10 = –5y –5–5 –5–5 –2 = y or Since y is multiplied by –5, divide both sides by –5 to undo the multiplication. y = –2

7. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Solve 4 + = 9. Solving Two-Step Equations Using Multiplication Step 1: – 4 Step 2: m = 35 Since m is divided by 7, multiply both sides by 7 to undo the division. m7m7 4 + = 9 m7m7 = 5 m7m7 Note that m is divided by 7. Then 4 is added. Work backward: Since 4 is added to, subtract 4 from both sides. m7m7 (7) = 5(7) m7m7

8. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Solve 14 = – 3. Solving Two-Step Equations Using Multiplication Step 1: + 3 Step 2: 34 = z z is divided by 2, multiply both sides by 2 to undo the division. z2z2 14 = – 3 z 12 17 = z2z2 Since 3 is subtracted from t, add 3 to both sides to undo the subtraction. z2z2 (2)17 = (2) z2z2

9. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Donna buys a portable DVD player that costs $120. She also buys several DVDs that cost $14 each. She spends a total of $204. How many DVDs does she buy? Consumer Math Application Let d represent the number of DVDs that Donna buys. That means Donna can spend $14d plus the cost of the DVD player. cost of DVD player cost of DVDs total cost += $12014d$204 +=

10. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations Donna buys a portable DVD player that costs $120. She also buys several DVDs that cost $14 each. She spends a total of $204. How many DVDs does she buy? Example Continued $12014d$204 += 120 + 14d = 204 –120 14d = 84 14 d = 6Donna purchased 6 DVDs.

11. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations John buys an MP3 player that costs $249. He also buys several songs that cost $0.99 each. He spends a total of $277.71. How many songs does he buy? Let s represent the number of songs that John buys. That means John can spend $0.99s plus the cost of the MP3 player. cost of MP3 player cost of songs total cost += $2490.99s$277.71 +=

12. Evaluating Algebraic Expressions 1-9 Solving Two-Step Equations 249 + 0.99s = 277.71 –249 0.99s = 28.71 s = 29John purchased 29 songs. John buys an MP3 player that costs $249. He also buys several songs that cost $0.99 each. He spends a total of $277.71. How many songs does he buy? $2490.99s$277.71 += 0.99s = 28.71 0.99