Download one step equations powerpoint

ONE STEP
EQUATIONS
Students will use
inverse operations to
solve one-step
equations.
3p = - 27
b
 12
3
ONE-STEP EQUATIONS
An equation is like a balance scale
because it shows that two
quantities are equal.
What you do to one side of the equation must also
be done to the other side to keep it balanced.
Keep the scale balanced.
If we add 3
apples to
this side…
What must
we do to
this side?
Keep the scale balanced.
If we subtract 3
bananas from
this side…
What must
we do to
this side?
ONE STEP EQUATIONS
To solve one step equations, you need to
ask three questions about the equation:
• What is the variable?
• What operation is performed on the variable?
• What is the inverse operation? (The one that will
“undo” what is being done to the variable)
INVERSE OPERATIONS
The inverse operation of addition is…
SUBTRACTION
The inverse operation of subtraction is…
ADDITION
The inverse operation of multiplication is…
DIVISION
The inverse operation of division is…
MULTIPLICATION
1-Step Equations with
addition
Example 1 Solve x + 3 = 9
What is the variable?
The variable is x.
What operation is being performed on the variable?
What is the inverse operation?
Subtraction.
Using the subtraction
property of equality,
subtract 3 from both
sides of the
equation.
x+3=9
-3 -3
x = 6
You can check
ALL answers.
Start by writing the original problem.
Plug in your answer.
Addition.
The subtraction
property of equality
tells us to subtract
the same thing on
both sides to keep
the equation equal.
x+3=9
6 +3=?
9
CORRECT!
Do/UNDO Approach
X=6
9
Inverse
UNDO
9
9
Practice: 1-step Equations with addition
1. m + 9 = 3
-9 -9
m = -6
check: -6 + 9 = ?
3=3
2. j + (-3) = 1
- (-3) - (-3)
j= 4
check: 4 + (-3) = ?
1=1
3. g + 4 = -12
-4 -4
4. c + 5 = 0
-5 -5
g = -16
c= -5
check: -16 + 4 = ?
-12 = -12 
check: - 5 + 5 = ?
0 =0
1-Step Equations with
subtraction
What is the variable? The variable is x.
What operation is being performed on the variable? Subtraction.
What is the inverse operation? Addition.
The addition
Using the
property of
x–4=7
addition property
equality tells
+
4
+
4
of equality, add 4
us to add the
to both sides of
same thing on
x = 11
the equation.
both sides to
Check your work!
keep the
equation
x–4=7
equal.
Plug in
your
answer.
11 – 4 = ?
7
CORRECT!
Do/Undo Approach
Inverse
UNDO
Practice: 1-step Equations with subtraction
1. f – 3 = - 5
+3 +3
2. n – 18 = 2
+ 18 +18
f = -2
n = 20
check: -2 – 3 = ?
-5 = -5 
check: 20 – 18 = ?
2=2
3. g – 8 = -2
+8 +8
4. m – 11 = 1
+ 11 +11
g=6
m = 12
check: 6 – 8 = ?
-2 = -2 
check: 12 – 11 = ?
1=1
1-Step Equations with
multiplication
Example 3 Solve 2x = 12
What is the variable? The variable is x.
What operation is being performed on the variable? Multiplication.
What is the inverse operation? Division
Using the division
property of
equality, divide
both sides of the
equation by 2.
2x = 12
2
2
x = 6
CHECK:
2x = 12
2(6) = ?
12
The division
property of equality
tells us to divide
the same thing on
both sides to keep
the equation equal.
REMEMBER:
The fraction
means DIVIDE!
CORRECT!
Do/Undo Approach
Inverse
UNDO
Practice: 1-step Equations with multiplication
1. 3a = -18
3
3
a = -6
Check: 3 (-6) = ?
-18 = -18 
3. 5m = -45
5
5
m = -9
Check: 5 (-9) = ?
-45 = -45 
2. -4n = -32
-4
-4
n=8
Check: -4 (8) = ?
-32 = -32 
4. -3x = 3
-3
-3
x = -1
Check: -3 (-1) = ?
3=3
1-Step Equations with
division
Example 4 Solve
What is the variable?
The variable is x.
What operation is being performed on the variable? Division.
What is the inverse operation? Multiplication
Using the
multiplication
property of
equality, multiply
both sides of the
equation by 6.
CHECK:
x
6•
= 8 •6
6
x = 48
x
6
The multiplication
property of
equality tells us to
multiply the same
thing on both
sides to keep the
equation equal.
=8
48
6
8
=?
Correct!
Do/Undo Approach
48
Inverse
UNDO
Practice: 1-step Equations with division
b
1. (3)  6 (3)
3
b = 18
Check: 18  ?
3
6=6
x
 9 (-4)
2.(-4)
4
x = -36
Check: 36  ?
4
9=9
x
 2(-5)
3.(-5)
5
k
 1(-8)
4. (-8)
8
x = 10
10
?
Check:
5
-2 = -2 
k = -8
8
?
Check:
8
1 = 1
Summary
When solving one-step equations,
always use the “inverse operation” to
undo the operation that is done on
the variable.
ALWAYS CHECK YOUR WORK!
Solve one-step equations.
1 Read the problem and connect it to the equation.
2 Solve for the variable. Hint: Use the inverse operation.
3
Check and interpret the solution. Hint: Answer the question.
1. Isabella is baking muffins. The recipe calls for
8 cups of sugar. Isabella has already added 3
cups of sugar. How many more cups of sugar
does she need to add?
c+38
3 3
c5
c+3=8
5+3=8
8=8
5 cups of sugar
Isabella needs to add __________________.
3. Shannon had some money in her pocket. She
received $4 for school supplies. She now has
$11. How much money did she start with?
m + 4  11
4 4
m7
m + 4 = 11
7 + 4 = 11
11 = 11
$7
Shannon started with __________________.
2. Yesterday, Samuel had $7. He was given
more money today and now has $10. How
much money was Samuel given today?
m + 7  10
7 7
m3
m + 7 = 10
3 + 7 = 10
10 = 10
$3
Samuel was given ________________
today.
4. Jessie had a few marbles. He earned 5 of
them during a game and now has 8. How
many marbles did Jessie start with?
m+58
55
m3
m+5=8
3+5=8
8= 8
3 marbles
Jessie started with _____________________.
Solve one-step equations.
1 Read
Read
thethe
problem
problem
and
and
connect
connect
it to
it to
thethe
equation.
equation.
2 Solve
Solve
forfor
thethe
variable.
variable.
Hint:
Hint:
Use
Use
thethe
inverse
inverse
operation.
operation.
3
Check
Check
and
and
interpret
interpret
thethe
solution.
solution.
Hint:
Hint:
Answer
Answer
thethe
question
question
.
.
1. Binders cost $2 each. If Miguel has $12, how
many binders can he buy?
2b  12
2
2
b6
2b = 12
2(6) = 12
12 = 12
2. A box of pencils has 6 pencils inside. If Rosalina
has 24 pencils, how many boxes does she have?
6b  24
6
6
b4
6b = 24
6(4) = 24
24 = 24
6 binders
Miguel can buy ______________________.
4 boxes of pencils
She has ______________________.
3. Isabella gave out muffins to her 6 friends. If each
friend was given 4 muffins, how many muffins
did Isabella give out?
m
4. Ricky and his two friends earned money doing
chores for his neighbor. After splitting the money,
they each got $7. How much money did they
earn together?
m
6
4
4 ● m  6● 4
24
6
4
4
m  24
6=6
24 muffins
Isabella gave out ______________________.
7
3
21
7
3
m  21
7=7
$21
Ricky and his friends earned _____________.
3 ● m  7● 3
3
Solve one-step equations.
1 Read the problem and connect it to the equation.
2 Solve for the variable. Hint: Use the inverse operation.
3
Check and interpret the solution. Hint: Answer the question.
1. Larissa has 17 dollars. She gets her allowance.
Now she has 28 dollars. How much was her
allowance?
17 + a  28
17 + a = 28
 17
 17
17 + 11 = 28
a  11
28 = 28
$11
Larissa’s allowance is ______________________.
3. Hugh earns $8 for mowing lawns. Last month, he
earned $48. How many lawns did he mow?
8m  48
8
8
b6
8m = 48
8(6) = 48
48 = 48
2. A set of colored pencils has 45 pencils taken out.
There are currently 29 pencils left. How many
pencils were there originally?
p  45 = 29
p  45  29
74  45 = 29
+ 45 + 45
29 = 29
n  74
74 pencils in the set originally.
There were __________________
4. Thomas and his 5 friends made cookies. They
shared them equally and each got 13. How many
cookies did they make altogether?
c
6 ● 6  13 ● 6
c  78
m
 13
6
78
 13
6
13 = 13
6 lawns
Hugh mowed ______________________.
78 cookies
Thomas and his friends made __________________.