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LESSON 10-5 Warm Up Lesson 10-5 Warm-Up ALGEBRA READINESS LESSON 10-5 Warm Up Lesson 10-5 Warm-Up ALGEBRA READINESS “Solving Multi-Step Equations” (10-5) What are the steps for solving a multi-step equation? Step 1: Clear the equation of fractions and decimals. You can clear decimals by using the decimal that has the most digits after it and moving all of the decimals that number of jumps to the right. Example: 0.5a2 + 0.875 = 13.25 Since 0.875 is the greatest number of place values from the end (3), jump all of the decimals 3 places to the right, so 0.5a2 + 0.875 = 13.25 is the same as 500a2 + 875 = 13,250 • • • Step 2: Use the Distributive Property to remove parenthesis if you can’t simplify the problem within them. Example: 4 (25) = 4 (20 + 5) = 4 • 20 + 4 • 5 = 80 + 20 = 100 Step 3: Combine like terms on each side. Examples: 4x + 5x = 9x 8a – 5a = 3a Step 4: “Undo” (since you’re working backwards) addition and subtraction. t – 7 + 7 = 20 + 7 Examples: 2x + 5 – 5 = 10 – 5 4 Step 5: Undo multiplication and division. 4 • t = 20 Examples: 2x = 10 • 4 1 4 2 2 ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Additional Examples Solve 2c + 2 + 3c = 12. 2c + 2 + 3c = 12 2c + 3c + 2 = 12 Commutative Property Simplify. 5c + 2 = 12 –2 –2 Subtraction Property of Equality 5c + 0 = 10 5c = 10 Simplify. 5c 5 = 10 5 1c = 2 Use the Division Property of Equality to isolate the variable (get the letter by itself). Simplify. 1 1 Identity Property of Addition 2 1 Check 2c + 2 + 3c = 12 2(2) + 2 + 3(2) 12 12 = 12 Substitute 2 for c. The solution checks. ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Additional Examples Eight cheerleaders set a goal of selling 424 boxes of cards to raise money. After two weeks, each cheerleader has sold 28 boxes. How many more boxes must each cheerleader sell? Words 8 cheerleaders • Let Equation 8 28 boxes per cheerleader additional + boxes per = 424 boxes cheerleader x = the number of additional boxes. • (28 + x) = 424 ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Additional Examples (continued) 8(28 + x) = 424 8 • 28 + 8 • x = 424 224 + – 224 0 + 8x = 424 – 224 Distributive Property Simplify. Use the Subtraction Property of Equality. 8x = 200 Simplify. 8x 200 = 8 8 Division Property of Equality 1 x = 25 Simplify. Each cheerleader must sell 25 more boxes. ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Additional Examples Solve 3a + 6 + a = 90 4a + 6 = 90 -6 - 6 Combine like terms (3a + 1a). 4a Simplify. = 84 4a + 0 = 84 4 4 1 a = 21 Divide each side by 4. Simplify. Check: 3a + 6 + a = 90 3(21) + 6 + 21 90 63 + 6 + 21 90 Substitute 21 for a. 90 = 90 ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Additional Examples Solve 3x + x = 17 2 5 Method 1: Finding common denominators 3x x + 2 5 3 1 x + 2 5x 15 2 x + 10 10 x 17 10 x 1 1 = 17 = 17 Rewrite the equation. = 17 A common denominator of 2 and 5 is 10. = 17 Combine like terms. 3 1 10 ( 17 x) = 17 ( 10 ) 17 10 1 17 1 1 1 1 x = 10 1 Multiply each side by the reciprocal of 17 , which is 10 . 10 17 Simplify. ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Additional Examples (continued) Method 2: Multiply both sides by the common denominator to clear the fractions. 3x x + = 17 2 5 3x x 10( 2 + 5 ) = 10(17) Multiply each side by 10, a common multiple of 2 and 5. 2 5 10 3x 10 ( x ) = 10( 17 ) ( ) + 1 1 1 2 1 5 1 1 15x Use the Distributive Property. + 17x 2x = 170 Simplify. = 170 Combine like terms. 17x 170 = 17 17 Divide each side by 17 to isolate the x. 1 x = 10 Simplify. ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Additional Examples Solve 0.6a + 18.65 = 22.85. 0•6 0• a + 18•65• = 22•85• 60a + 1865 = 2285 - 1865 - 1865 60a + 0 = 420 60a 60 = 420 60 The greatest number of decimal places is two places, so move each decimal two places to right. Simplify. Subtract 1865 from each side. Simplify. Divide each side by 60 to isolate the a. 1a = 7 Simplify. ALGEBRA READINESS Solving Multi-Step Equations LESSON 10-5 Lesson Quiz Solve the following equations. 1. 2m + 4 – 8m = 28 m = –4 2. 2(f – 1) + f = 37 f = 13 3. 4.5(4x – 12) = 144 x = 11 4. Jasmine earns a certain amount per hour for the first 40 hours worked in a week. Each hour she works over 40 in one week, she earns an additional $4.50 per hour. If Jasmine works 46 hours one week and earns $383.50 that week, how much does she earn per hour for the first 40 hours? $7.75 per hour ALGEBRA READINESS