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10-3 Solving Two-Step Equations Problem of the Day Janet used a pedometer to count her steps. The first day and third day she took exactly the same number of steps. The second day she took 1,739 steps. If she took 6,125 steps in all those 3 days, how many steps did she take the first day? 2,193 steps

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10-3 Solving Two-Step Equations

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10-3 Solving Two-Step Equations MA.6.A.3.3 Works backward with two-step functions rules to undo expressions. Also MA.6.A.3.2 Solving Two-Step Equations

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10-3 Solving Two-Step Equations Essential Question: How are equations applied in the real world? Solving Two-Step Equations

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10-3 Solving Two-Step Equations Warm Up – Refresh your memory: Solve each equation. 1. 15x = 225 2. y + 2 = 10 Find the value of each expression. 3. 18 – 6 3 5 4. 7 + 3 (16 4) – 2 x = 15 y = 8 8 17

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10-3 Solving Two-Step Equations Solve each equation. Solving Two-Step Equations 18 + 3x = 30 – 18 –18 3x = 12 x = 4 Subtract 18 from both sides to undo the addition. Divide both sides by 3 to undo the multiplication. 3x33x3 = 12 3

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10-3 Solving Two-Step Equations Check 18 + 3x = 30 18 + 3(4) 30 ?=?= ?=?= ?=?= 18 +12 30 30 Substitute 4 for x in the equation. 4 is the solution.

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10-3 Solving Two-Step Equations Undo operations in the reverse of the Order of Operations. First undo addition or subtraction. Then undo multiplication or division. Helpful Hint

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10-3 Solving Two-Step Equations – 2 = 1 + 2 +2 = 3 Add 2 to both sides to undo the subtraction. Solve. Check the answer. x = 9 Multiply both sides by 3. x3x3 x3x3 x3x3 3 · = 3 · 3 x3x3

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10-3 Solving Two-Step Equations ?=?= ?=?= ?=?= Substitute 9 for x in the equation. 9 is the solution. Check – 2 = 1 x3x3 – 2 1 9393 3 – 2 1 1

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10-3 Solving Two-Step Equations Solve each equation. Check It Out: Example 1A 12 + 3x = 27 – 12 –12 3x = 15 x = 5 Subtract 12 from both sides to undo the addition. Divide both sides by 3 to undo the multiplication. 3x33x3 = 15 3

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10-3 Solving Two-Step Equations Check Check It Out: Example 1A Continued 12 + 3x = 27 12 + 3(5) 27 ?=?= ?=?= ?=?= 12 +15 27 27 Substitute 5 for x in the equation. 5 is the solution.

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10-3 Solving Two-Step Equations Check It Out: Example 1B – 1 = 2 + 1 +1 = 3 Add 1 to both sides to undo the subtraction. Solve. Check the answer. x = 6 Multiply both sides by 2. x2x2 x2x2 x2x2 2 · = 2 · 3 x2x2

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10-3 Solving Two-Step Equations Check It Out: Example 1B Continued ?=?= ?=?= ?=?= Substitute 6 for x in the equation. 6 is the solution. Check – 1 = 2 x2x2 – 1 2 6262 3 – 1 2 2

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10-3 Solving Two-Step Equations Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy? Consumer Math Application Write a two-step equation to represent the situation. Let x represent the number of CDs Nancy can buy. cost of a CD times the number of CDs = The equation 15x + 12 = 87 represents the situation. cost of headphones total cost + 15x12 + 87 =

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10-3 Solving Two-Step Equations Solve the equation. 15x + 12 = 87 – 12 –12 15x = 75 15 x = 5 Nancy can buy 5 CDs. Subtract 12 from both sides. Divide both sides by 15. Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy?

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10-3 Solving Two-Step Equations Check It Out: Example 2B Write a two-step equation to represent the situation. Let d represent the number of days he rented the car. cost of rental fee times number of days = The equation 20d + 25 = 165 represents the situation. cost of mileage total cost + 20d25 + 165 = Jack rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $165.00. For how many days did he rent the car?

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10-3 Solving Two-Step Equations Check It Out: Example 2B Jack rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $165.00. For how many days did he rent the car? 20d + 25 = 165 – 25 – 25 20d = 140 20 d = 7 Jack rented the car for 7 days. Subtract 25 from both sides. Divide both sides by 20. Solve the equation.

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10-3 Solving Two-Step Equations Additional Example 3: Working Backward with Function Rules The function rule is 5 minus output The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11. times input 4equals 5 – y x x 4=

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10-3 Solving Two-Step Equations Additional Example 3 Continued 5x – 4 = 11 + 4 + 4 5x = 15 5 5 x = 3 The input value is 3. Use the function rule and the given output value to write an equation. Divide both sides by 5. Add 4 to both sides to undo the subtraction. The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.

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10-3 Solving Two-Step Equations Additional Example 3 Continued Check Substitute the input value into the rule. 5(3) – 4 = 15 – 4 = 11 check The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.

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10-3 Solving Two-Step Equations Check it Out: Example 3 The function rule is 6 minus output The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9. times input 3equals 6 – y x x 3=

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10-3 Solving Two-Step Equations Check it Out Example 3 Continued 6x – 3 = 9 + 3 + 3 6x = 12 6 6 x = 2 The input value is 2. Use the function rule and the given output value to write an equation. Divide both sides by 6. Add 3 to both sides to undo the subtraction. The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.

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10-3 Solving Two-Step Equations Check it Out Example 3 Continued Check Substitute the input value into the rule. 6(2) – 3 = 12 – 3 = 9 check The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.

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10-3 Solving Two-Step Equations Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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10-3 Solving Two-Step Equations Lesson Quiz Solve each equation. Check your answer. 1. – 7 = 1 2. 22x + 11 = 143 3. 4. x = 6 x = 96 x = 26 x = 5 x + 9 5 = 7 9x – 6 = 39 5. In two days, Yasmine drove 505 miles to visit her cousin. The first day, she drove 230 miles. The next day Yasmine drove 5 hours at a constant speed. How fast did Yasmine drive on the second day? 55 mi/h x 12

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10-3 Solving Two-Step Equations 1. Solve 4x + 3 = 27. A. x = 6 B. x = 7.5 B. x = 8 B. x = 96 Lesson Quiz for Student Response Systems

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10-3 Solving Two-Step Equations 3. Solve. A. x = 15 B. x = 20 C. x = 60 D. x = 100 Lesson Quiz for Student Response Systems

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