Download 2 nd step

Observation…
How is problem #1
different from problem #2?
1)
214 = y + 112
How is problem #3
different from problem #4?
3)
This is a one-step equation.
This is a one-step equation.
2)
214 = 2y + 112
This is a two-step equation.
5x = 20
4)
5x - 25 = 20
This is a two-step equation.
Solving equations in two steps
Goal:
1st step:
2nd step:
Tips:
Solving equations in two steps
Goal: get the variable (letter) by itself.
1st step:
2nd step:
Tips:
undo addition or
subtraction
undo multiplication
or division
Read the
equation.
SHOW
YOUR
WORK!
3x + 10 = 37
-10 -10
3x
3
x
= 27
3
=9
Draw a line
down the
equal sign.
x - 8 = 12
4
+8 +8
4 x
= 20  4
4
x = 80
Cross #s out
when they’re
cancelled.
Circle your
answer.
12-1 Solving Two-Step Equations
Check It Out: Example 1A
Solve. Check the answer.
7c + 6 = 48
7c + 6 = 48
–6
7c
–6
= 42
7c = 42
7
7
c=6
Course 2
Subtract 6 from both sides.
Divide both sides by 7.
12-1 Solving Two-Step Equations
Additional Example 1A: Solving Two-Step Equations
Using Division
Solve. Check each answer.
9c + 3 = 39
9c + 3 = 39
–3
9c
–3
= 36
9c = 36
9
9
c=4
Course 2
Subtract 3 from both sides.
Divide both sides by 9.
12-1 Insert
TitleEquations
Here
SolvingLesson
Two-Step
Check It Out: Example 2A
Solve.
8+ y
2
y
8+ 2
–8
y
2
y
(2) 2
= 48
= 48
–8
= 40
Subtract 8 from both sides.
= (2)40
Multiply both sides by 2.
y = 80
Course 2
12-1 Insert
TitleEquations
Here
SolvingLesson
Two-Step
Check It Out: Example 2B
Solve.
x – 31 = 19
5
x – 31 = 19
5
+31 +31
x
= 50
5
x
(5) 5
= (5)50
x = 250
Course 2
Add 31 to both sides.
Multiply both sides by 5.
12-1 Solving Two-Step Equations
Additional Example 3: Consumer Math Application
Jamie rented a canoe while she was on vacation. She paid a
flat rental fee of $85.00, plus $7.50 each day. Her total cost
was $130.00. For how many days did she rent the canoe?
Let d represent the number of days she rented the canoe.
7.5d + 85 = 130
– 85 –85
7.5d
= 45
7.5d = 45
7.5
7.5
Subtract 85 from both sides.
Divide both sides by 7.5.
d =6
Jamie rented the canoe for 6 days.
Course 2
12-1 Insert
TitleEquations
Here
SolvingLesson
Two-Step
Check It Out: Example 3
Jack’s father 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?
Let d represent the number of days he rented the car.
20d + 25 = 165
– 25 – 25
Subtract 25 from both sides.
20d
= 140
20d = 140
Divide both sides by 20.
20
20
d =7
Jack’s father rented the car for 7 days.
Course 2