Problem of the Day

1
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
2
Solving Two-Step Equations
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
4
Solving Two-Step Equations
Essential Question How are equations applied
in the real world?
5
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
6
Solving Two-Step Equations
Solve each equation.
18 3x 30
18 3x 30
18 18
Subtract 18 from both sides to undo the addition.
3x 12
Divide both sides by 3 to undo the multiplication.
x 4
7
Check
18 3x 30
Substitute 4 for x in the equation.
?
18 3(4)
30
?
18 12 30
?
30 30
4 is the solution.
8
(No Transcript)
9
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.
2 2
x 3
3
Multiply both sides by 3.
x 9
10
Check
x 3
2 1
9 3
Substitute 9 for x in the equation.
?
2 1
?
3 2 1
?
9 is the solution.
1 1
11
Check It Out Example 1A
Solve each equation.
12 3x 27
12 3x 27
12 12
Subtract 12 from both sides to undo the addition.
3x 15
Divide both sides by 3 to undo the multiplication.
x 5
12
Check It Out Example 1A Continued
Check
12 3x 27
Substitute 5 for x in the equation.
?
12 3(5)
27
?
12 15 27
?
27 27
5 is the solution.
13
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.
1 1
x 2
3
Multiply both sides by 2.
x 6
14
Check It Out Example 1B Continued
Check
x 2
1 2
6 2
Substitute 6 for x in the equation.
?
1 2
?
3 1 2
?
6 is the solution.
2 2
15
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.
16
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 12 87
12 12
Subtract 12 from both sides.
15x 75
Divide both sides by 15.
15x 75
15
15
x 5
Nancy can buy 5 CDs.
17
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?
Write a two-step equation to represent the
situation. Let d represent the number of days he
rented the car.
cost of mileage
cost of rental fee times number of days
total cost




20d
25
165
The equation 20d 25 165 represents the
situation.
18
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?
Solve the equation.
20d 25 165
25 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.
19
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
output
5
times
4
equals
input
minus
y
5
x
4

x

20
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.
4 4
5x 15
5x 15
Divide both sides by 5.
5
5
x 3
The input value is 3.
21
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
22
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
output
6
times
3
equals
input
minus
y
6
x
3

x

23
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.
3 3
6x 12
6x 12
Divide both sides by 6.
6
6
x 2
The input value is 2.
24
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
25
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
26
Lesson Quiz
Solve each equation. Check your answer. 1.
7 1 2. 22x 11 143 3. 4.
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
27
Lesson Quiz for Student Response Systems
1. Solve 4x 3 27. A. x 6 B. x
7.5 B. x 8 B. x 96
28
Lesson Quiz for Student Response Systems
3. Solve . A. x 15
B. x 20 C. x 60 D. x 100