Transcript Writing and Solving One-Step Equations

Writing and Solving One-Step
Equations
Using Properties of Equality to Solve
Equations
Vocabulary
• An equation is a statement of equality.
• Inverse operations are opposite operations that “undo” part of
an equation.
• Isolating the variable removes all values from the equation but
the variable and the solution.
• A solution is a value that makes the equation true, or balanced.
If you substitute this value
into the original equation, it makes a TRUE
statement!
What an Equation Looks Like
=
30 lbs
4+
Something = Something
Addition Property of Equality
5 + 3 = 8
5 + 3 +2 = 8 + 2
If a = b
then a + c = b + c
Subtraction Property of Equality
5 + 3 = 8
(5 + 3) - 2 = 8 - 2
If a = b
then a - c = b - c
This is saying…….
“If I have two things that are
equal, and I add the same thing
to each value, they will
STILL be equal!
This is saying…….
“If I have two things that are
equal, and I subtract the same thing
from each value, they will
STILL be equal!
Multiplication Property of Equality
5 + 3 = 8
(5 + 3) x 2 = 8 x 2
If a = b
then a x c = b x c
This is saying…….
“If I have two things that are
equal, and I multiply each value
by the same thing, they will
STILL be equal!
Division Property of Equality
5 + 3 = 8
(5 + 3) ÷ 2 = 8 ÷ 2
This is saying…….“If I have two things that are
If a = b
and I divide each value by the same thing, they will
then a ÷ c = b ÷ c equal,
STILL be equal!
Working the Process
We will begin with basic equations that have obvious
solutions. As you work through each one, ask yourself
this series of solving questions:
 What is the variable I am trying to isolate?
 What operation does the equation show?
 What is the inverse operation I will use to solve for the variable?
Of course we can
see the answer.
This lesson is
about PROCESS!
We used the subtraction
property of equality to
solve.
x + 7 = 25
-7 = -7
x = 18
x + 0 = 18 Do you see another property?
We Are Working A Process!!
x - 19 = 34
+ 19 +19
x = 53
Leave the variable
on the same side!
24 = n + 17
- 17
- 17
7 = n
 What is the variable I am trying to isolate?
 What operation does the equation show?
 What is the inverse operation I will use to solve for the variable?
How will integers affect the process????
REWRITE!!!
n + 12 = -14
+(-12) +(-12)
n
= -26
Does -26 + 12 = -14 ?
-12 + n = 4
+ 12
+12
n = 16
Does -12 + 16 = 4 ?
n – (-5) = 27
n + 5 = 27
+ (-5) +(-5)
n = 22
22 + 5 = 27
Word Problems to Equations
Claire had n books. After buying eight more, she
then had 24 books. How many did she start
with?
n + 8 = 24
- 8 = -8
n
= 16
Word Problems to Equations
A CD costs $14.95. This is $7.55 less than the
cost of a DVD. Write and solve a subtraction
equation to find the cost of the DVD.
Equation and Solution:
n - $7.55 = $14.95
+ 7.55 = + 7.55
n
= $22.50
Multiplication Equations….

What is the variable? What operation is used? What is the INVERSE operation I need?
4n = 84
4
4
n = 21
91 = 7y
(7)
13
(7)
12w = 108
12
12
= y
It matters where the solving value is placed!!!
Try to use a division bar, not the ÷
w
= 9
How will integers affect the process?
-108 = -4n
-4 -4
27 = n
.5n = -25.5
.5
.5
-255
5
n = -51
𝟒
(− )
𝟑
-¾n=
𝟒
12 (− 𝟑)
n = -9
𝟒
𝟗
(− )( −
= 𝟏𝟐
𝟑
𝟏
??????
Selling the Paintings
p
45
p
p
3p
=
$45
= $45
3
3
p = $15
There are three paintings, all worth the same amount of money. The
total for all three is $45. What is each painting worth? Write a
multiplication equation. Solve.
If I have $35 dollars to spend over 5 days,
how much could I spend each day? Write a
multiplication equation that requires you to
divide for the solution.
for 5 days? = total amount of $$$$
5n = 35
5n  35
5n 35

5
5
I would divide to solve this
multiplication equation.
n  $7
Working with Division
We want our coefficient to have a value of 1.
WHERE you place your solving value is important!
( 2) r = 20 (2)
2
1 r = 40
(6)b = 24(6)
6
1 b = 144
(4) 6 = n(4)
4
24 =1n
Let’s add integers to these.
( 14)
𝑛
14
= −7 (14)
1 n = -98
( -40)
𝑛
−40
= 80 (-40)
1n = -3200
( -12) 𝑛 = -4(-12)
−12
1n = 48
I have a LOT of pizzas to eat this week.
It will take me 7 days, and I will eat 4 pizzas
each day. How many did I start with? Write a division
problem.
All the pizzas
divided over 7 days
p
4
7
 4 pizzas each day
7p
 7(4)
7
p  28 pizzas
Let’s take our multiplication equation and use different “given”
values to write a division equation.
If I have found a treasure chest. I don’t know how much
money is in it. If I spend it over five days, I will spend
$7 each day.
$$
5
Split up over 5 days?
(5)
= 7 each day
n
 $7 (5)
5
n  $35
I would multiply to solve this
division equation.
A board that measures 19.5 meters in length is cut into two
pieces. One piece measures 7.2 meters. Write and solve an
equation to find the length of the other piece.
Mixed Operations
19.5 = 7.2 + n
- 7.2 -7.2
12.3 = n
It takes 43 facial muscles to frown. This is 26 more muscles
than it takes to smile. Write and solve an equation to find
the numbers of muscles it takes to smile.  
26 + s = 43
- 26
-26
s = 17 muscles
Writing Equations…………Using key words to determine the operation
Meghan’s bowling score was 39 points
less than Charmaine’s. Meghan’s
score was 109. What was Charmaine’s score?
Let’s keep looking for clues……..Meghan’s score was 109. This is LESS THAN
Charmain’s score.
Think….Meghan’s SCORE is 39 LESS THAN Charmaine’s score
109
= c -
39
+ 39__
+ 39_
148
= Charmaine’s score
Chen is buying a ham. He wants to divide it into 6.5 ounce servings for 12
people. Write and solve the equation to find how much he should buy to have this
much for each person.
ℎ
= 6.5
12
The total time to burn a CD is 18 minutes.
Last weekend Demitri spent 90 minutes burning CDS. Write and
solve a multiplication equation to find the number of CDs Demitri burned
last weekend. How can you check you solution?
18 times what number is 90??
18𝑛 = 90
18 18
𝑛=5
9(10)
9(2)
A male gorilla weighs 379 pounds on average. This is 181 pounds more than the
weight of the average female gorilla. Write and solve and addition equation to find
the weight of an average female gorilla
181 + w = 379
-181
-181
w = 198
Extending the Solving Process



Before we write and solve multi-step equations to solve word
problems, we will practice the correct algorithm for solving
multi-step equations.
Remember, we are working towards perfecting a process……..
Show all work and be very thorough in your thinking!
Problem:
Identify the variable to isolate:
Identify the first solving step:
Solve to isolate the term:
Solve for solution:
𝑥
+ 7 = 12
10
−7 = −7
𝑥
=5
10
𝑥
(10)
= 5(10)
10
x = 50
Problem:
Identify the variable to isolate:
Identify the first solving step:
Solve, step 1:
Solve for solution:
𝑥
+ 11 = 13
2
−11 = −11
𝑥
=2
2
(2)𝑥
= 2(2)
2
x=4
Problem:
Identify the variable to isolate:
Identify the first solving step:
Solve, step 1:
6x +2 = 8
−2 = −2
6𝑥 = 6
Solve for solution:
6𝑥 6
=
6
6
x=1
𝑥
2
+5 =12
− 5 = −5
𝑥
=7
2
(2)𝑥
= 7(2)
2
x = 14
𝑥
10
+3 = 33
− 3 = −3
𝑥
(10)
= 30 (10)
10
x = 300
5x +6 = 11
−6 = −6
5𝑥 = 5
5𝑥 5
=
5
5
x=1
Please turn your notes over and copy these two equations.
3(x +5) = 30
3𝑥 + 15 = 30
− 15 = −15
3𝑥 =15
3𝑥 15
=
3
3
x=5
3(2x +7) − 4 = 29
6𝑥 + 21 − 4 = 29
6𝑥 + 17 = 29
− 17 = −17
6𝑥 =12
6𝑥 12
=
6
6
x=2


We have practiced the correct process for solving multi-step
equations to prepare for writing and solving these equations
for word problems.
The focus of tonight’s homework will be the process (of
course ). We will start with a few word problems to apply
this skill. The class will do these together.
Homework?
• Your homework will be over the solving PROCESS. We will
continue to work together tomorrow to identify equations that
match certain word problems.