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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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**Solving Two-Step Equations**

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**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

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**Solving Two-Step Equations**

Essential Question: How are equations applied in the real world?

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**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 (16 4) – 2 x = 15 y = 8 8 17

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**Solving Two-Step Equations**

Solve each equation. 18 + 3x = 30 18 + 3x = 30 – –18 Subtract 18 from both sides to undo the addition. 3x = 12 3x 3 = 12 Divide both sides by 3 to undo the multiplication. x = 4

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**Check 18 + 3x = 30 Substitute 4 for x in the equation. 18 + 3(4) 30**

? = 30 ? = ? = 4 is the solution.

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**Undo operations in the reverse of the Order of Operations**

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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**Solving Two-Step Equations**

Solve. Check the answer. x 3 – 2 = 1 x 3 – 2 = 1 Add 2 to both sides to undo the subtraction. x 3 = 3 3 · = 3 · 3 x 3 Multiply both sides by 3. x = 9

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**Check x 3 – 2 = 1 9 3 Substitute 9 for x in the equation. – 2 1**

– 2 = 1 9 3 Substitute 9 for x in the equation. ? = – ? = 3 – ? = 9 is the solution.

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

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**Check It Out: Example 1A Continued**

Substitute 5 for x in the equation. 12 + 3(5) ? = 27 ? = ? = 5 is the solution.

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Check It Out: Example 1B Solve. Check the answer. x 2 – 1 = 2 x 2 – 1 = 2 Add 1 to both sides to undo the subtraction. x 2 = 3 2 · = 2 · 3 x 2 Multiply both sides by 2. x = 6

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**Check It Out: Example 1B Continued**

2 – 1 = 2 6 2 Substitute 6 for x in the equation. ? = – ? = 3 – ? = 6 is the solution.

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**Consumer Math Application**

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? 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 cost of headphones total cost + = 15x + 12 = 87 The equation 15x + 12 = 87 represents the situation.

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**Nancy saved $87 of the money she made babysitting**

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? Solve the equation. 15x = 87 – –12 Subtract 12 from both sides. 15x = 75 15x = 75 Divide both sides by 15. 15 15 x = 5 Nancy can buy 5 CDs.

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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 $ For how many days did he rent the car? 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 cost of mileage total cost + = 20d + 25 = 165 The equation 20d + 25 = 165 represents the situation.

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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 $ For how many days did he rent the car? Solve the equation. 20d + 25 = 165 – – 25 Subtract 25 from both sides. 20d = 140 20d = 140 Divide both sides by 20. 20 20 d = 7 Jack rented the car for 7 days.

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**Additional Example 3: Working Backward with Function Rules**

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. The function rule is 5 times input minus 4 equals output 5 x x – 4 = y

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**Additional Example 3 Continued**

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. Use the function rule and the given output value to write an equation. 5x – 4 = 11 Add 4 to both sides to undo the subtraction. 5x = 15 5x = 15 Divide both sides by 5. 5 5 x = 3 The input value is 3.

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**Additional Example 3 Continued**

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. Check Substitute the input value into the rule. 5(3) – 4 = 15 – 4 = 11 check

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Check it Out: Example 3 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. The function rule is 6 times input minus 3 equals output 6 x x – 3 = y

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**Check it Out Example 3 Continued**

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. Use the function rule and the given output value to write an equation. 6x – 3 = 9 Add 3 to both sides to undo the subtraction. 6x = 12 6x = 12 Divide both sides by 6. 6 6 x = 2 The input value is 2.

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**Check it Out Example 3 Continued**

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. Check Substitute the input value into the rule. 6(2) – 3 = 12 – 3 = 9 check

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**Lesson Quiz for Student Response Systems**

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 25 25

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**Solve each equation. Check your answer. 1. – 7 = 1 2. 22x + 11 = 143 **

Lesson Quiz Solve each equation. Check your answer. – 7 = 1 2. 22x + 11 = 143 3. 4. x 12 x = 96 x = 6 x + 9 5 = 7 x = 26 9x – 6 = 39 x = 5 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

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**Lesson Quiz for Student Response Systems**

1. Solve 4x + 3 = 27. A. x = 6 B. x = 7.5 B. x = 8 B. x = 96 27 27

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**Lesson Quiz for Student Response Systems**

3. Solve A. x = 15 B. x = 20 C. x = 60 D. x = 100 28 28

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2-2 Solving Two-Step Equations Warm Up Solve each equation. 1. 3 + x = 112. x – 7 = 19 3. 6x = 154. Find a common denominator. 5. 6. 8 26 12 Possible answer:

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