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
10-3 Solving Two-Step Equations
Solving Two-Step
Equations
10-3 Solving Two-Step Equations
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
10-3 Solving Two-Step Equations
Solving Two-Step Equations
Essential Question:
How are equations applied in
the real world?
10-3 Solving Two-Step Equations
Warm Up – Refresh your memory:
Solve each equation.
1. 15x = 225
x = 15
2. y + 2 = 10
y=8
Find the value of each expression.
3. 18 – 6 3
4. 7 + 3


5
8
(16  4) – 2
17
10-3 Solving Two-Step Equations
Solving Two-Step Equations
Solve each equation.
18 + 3x
18 + 3x
– 18
3x
= 30
= 30
–18
= 12
Subtract 18 from both sides to
undo the addition.
3x = 12
3
3
Divide both sides by 3 to undo
the multiplication.
x=4
10-3 Solving Two-Step Equations
Check
18 + 3x = 30
? 30
18 + 3(4)=
Substitute 4 for x in the
equation.
? 30
18 +12 =
? 30
30 =
4 is the solution.
10-3 Solving Two-Step Equations
Helpful Hint
Undo operations in the reverse of the
Order of Operations. First undo
addition or subtraction. Then undo
multiplication or division.
10-3 Solving Two-Step Equations
Solving Two-Step Equations
Solve. Check the answer.
x
–2= 1
3
x
–2= 1
3
+ 2 +2
x
= 3
3
3· x= 3·3
3
x=9
Add 2 to both sides to undo
the subtraction.
Multiply both sides by 3.
10-3 Solving Two-Step Equations
Check
x
–2 = 1
3
9
? 1
–2 =
3
?
=
3 –2
1
?
1 =
1
Substitute 9 for x in the
equation.
9 is the solution.
10-3 Solving Two-Step Equations
Check It Out: Example 1A
Solve each equation.
12 + 3x = 27
12 + 3x = 27
– 12
–12
3x = 15
Subtract 12 from both sides to
undo the addition.
3x = 15
3
3
Divide both sides by 3 to undo
the multiplication.
x=5
10-3 Solving Two-Step Equations
Check It Out: Example 1A Continued
Check
12 + 3x = 27
? 27
12 + 3(5)=
Substitute 5 for x in the
equation.
? 27
12 +15 =
? 27
27 =
5 is the solution.
10-3 Solving Two-Step Equations
Check It Out: Example 1B
Solve. Check the answer.
x
–1= 2
2
x
–1= 2
2
+ 1 +1
x
= 3
2
2· x= 2·3
2
x=6
Add 1 to both sides to undo
the subtraction.
Multiply both sides by 2.
10-3 Solving Two-Step Equations
Check It Out: Example 1B Continued
Check
x
–1 =2
2
6
? 2
–1 =
2
?
=
3 –1
2
?
2 =
2
Substitute 6 for x in the
equation.
6 is the solution.
10-3 Solving Two-Step Equations
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
15x
+
cost of
=
headphones
12
=
total cost
87
The equation 15x + 12 = 87 represents the situation.
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?
Solve the equation.
15x + 12
– 12
15x
15x
15
x
= 87
–12
= 75
= 75
15
=5
Nancy can buy 5 CDs.
Subtract 12 from both sides.
Divide both sides by 15.
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?
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
20d
+
cost of
mileage
=
25
=
total cost
165
The equation 20d + 25 = 165 represents the situation.
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?
Solve the equation.
20d + 25 = 165
– 25 – 25
20d
= 140
20d = 140
20
20
d =7
Subtract 25 from both sides.
Divide both sides by 20.
Jack rented the car for 7 days.
10-3 Solving Two-Step Equations
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
10-3 Solving Two-Step Equations
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.
5x – 4 = 11
+4
5x
+4
Use the function rule and the given
output value to write an equation.
Add 4 to both sides to undo the
subtraction.
= 15
5x = 15
5
5
x =3
The input value is 3.
Divide both sides by 5.
10-3 Solving Two-Step Equations
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
10-3 Solving Two-Step Equations
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
10-3 Solving Two-Step Equations
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.
6x – 3 =
+3
6x
9
+3
Use the function rule and the given
output value to write an equation.
Add 3 to both sides to undo the
subtraction.
= 12
6x = 12
6
6
x =2
The input value is 2.
Divide both sides by 6.
10-3 Solving Two-Step Equations
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
10-3 Solving Two-Step Equations
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
10-3 Solving Two-Step Equations
Lesson Quiz
Solve each equation. Check your answer.
x
1. 12 – 7 = 1
x = 96
2. 22x + 11 = 143
x=6
3. x + 9 = 7
x = 26
4. 9x – 6 = 39
x=5
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
10-3 Solving Two-Step Equations
Lesson Quiz for Student Response Systems
1. Solve 4x + 3 = 27.
A. x = 6
B. x = 7.5
B. x = 8
B. x = 96
10-3 Solving Two-Step Equations
Lesson Quiz for Student Response Systems
3. Solve
A. x = 15
B. x = 20
C. x = 60
D. x = 100
.