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.

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


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



Essential Question:

How are equations applied in the real world?



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


Solve each equation.


18 + 3x = 30

18 + 3x = 30

– 18 –183x = 12

x = 4

Subtract 18 from both sides to undo the addition.

Divide both sides by 3 to undothe multiplication.

3x3

= 12 3


Check

18 + 3x = 30

18 + 3(4) 30?=

?=

?=

18 +12 30

30 30

Substitute 4 for x in the equation.

4 is the solution.


Undo operations in the reverse of the Order of Operations. First undo addition or subtraction. Then undo multiplication or division.

Helpful Hint



– 2 = 1

– 2 = 1

+ 2 +2

= 3

Add 2 to both sides to undothe subtraction.

Solve. Check the answer.

x = 9

Multiply both sides by 3.

x3

x3

x3

3 · = 3 · 3 x3


?=

?=

?=


9 is the solution.

Check

– 2 = 1x3

– 2 193

3 – 2 1

1 1


Solve each equation.

Check It Out: Example 1A

12 + 3x = 27

12 + 3x = 27

– 12 –123x = 15

x = 5

Subtract 12 from both sides to undo the addition.

Divide both sides by 3 to undothe multiplication.

3x3

= 15 3


Check

Check It Out: Example 1A Continued

12 + 3x = 27

12 + 3(5) 27?=

?=

?=

12 +15 27

27 27


5 is the solution.


Check It Out: Example 1B

– 1 = 2

– 1 = 2

+ 1 +1

= 3

Add 1 to both sides to undothe subtraction.

Solve. Check the answer.

x = 6

Multiply both sides by 2.

x2

x2

x2

2 · = 2 · 3 x2


Check It Out: Example 1B Continued

?=

?=

?=


6 is the solution.

Check

– 1 = 2x2

– 1 262

3 – 1 2

2 2


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 timesthe number of CDs

=

The equation 15x + 12 = 87 represents the situation.

cost of headphones

total cost+

15x 12 + 87=


Solve the equation.

15x + 12 = 87 – 12 –1215x = 75

15x = 7515 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?


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 feetimes number of days

=

The equation 20d + 25 = 165 represents the situation.

cost of mileage

total cost+

20d 25 + 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?

10-3 Solving Two-Step EquationsCheck 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 = 14020d = 14020 20

d = 7

Jack rented the car for 7 days.

Subtract 25 from both sides.


Solve the equation.


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 4 equals

5 – yx x 4 =


Additional Example 3 Continued

5x – 4 = 11

+ 4 + 4

5x = 15

5x = 155 5x = 3

The input value is 3.

Use the function rule and the given output value to write an equation.


Add 4 to both sides to undo thesubtraction.



Additional Example 3 Continued

Check Substitute the input value into the rule.

5(3) – 4 = 15 – 4 = 11 check



Check it Out: Example 3

The function rule is

6 minus output


times input 3 equals

6 – yx x 3 =


Check it Out Example 3 Continued

6x – 3 = 9

+ 3 + 3

6x = 12

6x = 126 6x = 2

The input value is 2.

Use the function rule and the given output value to write an equation.


Add 3 to both sides to undo thesubtraction.



Check it Out Example 3 Continued

Check Substitute the input value into the rule.

6(2) – 3 = 12 – 3 = 9 check



Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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 + 95

= 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

x12


1. Solve 4x + 3 = 27.

A. x = 6

B. x = 7.5

B. x = 8

B. x = 96



3. Solve .

A. x = 15

B. x = 20

C. x = 60

D. x = 100


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.

Documents

equations ma

x3x3 slide

x2x2 slide

continued check

helpful hint slide

undo addition

cost of mileage total

cost of headphones total