Download solve an equation

Lesson 2.2: Solving Equations Using
Addition and Subtraction
Algebra 1 CP
Mrs. Mongold
Solving an equation

To solve an equation means to find all values of
the variable that make it true
Solving an equation

To solve an equation means to find all values of
the variable that make it true

Steps to solve an equation:
Solving an equation

To solve an equation means to find all values of
the variable that make it true

Steps to solve an equation:
◦ 1. Get the variable on one side of the equation
and get the numbers on the other side
Solving an equation

To solve an equation means to find all values of the
variable that make it true

Steps to solve an equation:
◦ 1. Get the variable on one side of the equation and
get the numbers on the other side
◦ 2. Check your answer in the original equation to make
sure it makes sense
Addition Property of Equality:
◦ If you add the same amount to each side
of the equal sign, the equation is true
Addition Property of Equality:
◦ If you add the same amount to each side
of the equal sign, the equation is true
 Think to yourself to “undo” subtraction you
do it’s opposite which is addition
Addition Property of Equality:
◦ If you add the same amount to each side
of the equal sign, the equation is true
 Think to yourself to “undo” subtraction you
do it’s opposite which is addition
Ex: m – 48 = 29
Subtraction Property of Equality:
◦ If you subtract the same amount from each
side, the equation is true
Subtraction Property of Equality:
◦ If you subtract the same amount from each
side, the equation is true
 Think to yourself to “undo” addition you do the
opposite which is subtraction
Subtraction Property of Equality:
◦ If you subtract the same amount from each
side, the equation is true
 Think to yourself to “undo” addition you do the
opposite which is subtraction
Example: 42 + d = 27
Your turn

Solve each equation
1. x+5 = 7
Your turn

Solve each equation
1. x+5 = 7
Your turn

Solve each equation
1. x+5 = 7
-5 -5
Your turn

Solve each equation
1. x+5 = 7
-5 -5
x=2
Your turn

Solve each equation
1. x+5 = 7
-5 -5
x=2
CHECK:
2+5=7
Your turn

Solve each equation
2. x + 3 = -4
Your turn

Solve each equation
2. x + 3 = -4
Your turn

Solve each equation
2. x + 3 = -4
-3
-3
Your turn

Solve each equation
2. x + 3 = -4
-3
-3
x = -7
Your turn

Solve each equation
2. x + 3 = -4
-3
-3
x = -7
CHECK:
-7+3=-4
Your turn

Solve each equation
3. x + 7 = 2
Your turn

Solve each equation
3. x + 7 = 2
How do I “undo”
addition?
Your turn

Solve each equation
3. x + 7 = 2
-7
-7
How do I “undo”
addition?
Your turn

Solve each equation
3. x + 7 = 2
-7
-7
x = -5
How do I “undo”
addition?
Your turn

Solve each equation
3. x + 7 = 2
-7
-7
x = -5
CHECK:
-5+7=2
How do I “undo”
addition?
Your turn

Solve each equation
4. 32 = r – 8
Your turn

Solve each equation
4. 32 = r – 8
How do I “undo”
subtraction?
Your turn

Solve each equation
4. 32 = r – 8
+8 = + 8
How do I “undo”
subtraction?
Your turn

Solve each equation
4. 32 = r – 8
+8 = + 8
40 = r
How do I “undo”
subtraction?
Your turn

Solve each equation
4. 32 = r – 8
+8 = + 8
40 = r
CHECK:
32 = 40 - 8
How do I “undo”
subtraction?
Your turn

Solve each equation
5. 7 = 42 + t
Your turn

Solve each equation
5. 7 = 42 + t
How do I move the 42? Is
it being added or
subtracted or something
else?
Your turn

Solve each equation
5. 7 = 42 + t
It’s positive so it’s like
adding…. To “undo”
addition we will subtract!!
Your turn

Solve each equation
5. 7 = 42 + t
-42 -42
It’s positive so it’s like
adding…. To “undo”
addition we will subtract!!
Your turn

Solve each equation
5. 7 = 42 + t
-42 -42
-35 = t
It’s positive so it’s like
adding…. To “undo”
addition we will subtract!!
Your turn

Solve each equation
5. 7 = 42 + t
-42 -42
-35 = t
t = -35
It’s positive so it’s like
adding…. To “undo”
addition we will subtract!!
What property is this?
Your turn

Solve each equation
5. 7 = 42 + t
-42 -42
-35 = t
t = -35
It’s positive so it’s like
adding…. To “undo”
addition we will subtract!!
What property is this?
- Symmetric
Your turn

Solve each equation
5. 7 = 42 + t
-42 -42
-35 = t
t = -35
CHECK:
7 = 42 + (- 35)
It’s positive so it’s like
adding…. To “undo”
addition we will subtract!!
What property is this?
- Symmetric
Your turn

Solve each equation
6. h – 12 = -27
Your turn

Solve each equation
6. h – 12 = -27
How do I “undo”
subtraction?
Your turn

Solve each equation
6. h – 12 = -27
+12
+12
How do I “undo”
subtraction?
Your turn

Solve each equation
6. h – 12 = -27
+12
+12
h = -15
How do I “undo”
subtraction?
Your turn

Solve each equation
6. h – 12 = -27
+12
+12
h = -15
CHECK:
-15 -12 = -27
How do I “undo”
subtraction?
Your turn

Solve each equation
7. x  3   1
2
4
Your turn

Solve each equation
7. x  3   1
2
4
How do I “undo”
subtraction?
Your turn

x
3
1

2
4
How do I “undo”
subtraction?
Your turn

x
3
1

2
4
1 3
x 
4 2
How do I “undo”
subtraction?
Oh no! A fraction…. Are we scared?
Your turn

x
3
1

2
4
1 3
x 
4 2
How do I “undo”
subtraction?
Oh no! A fraction…. Are we scared?
NO… fractions aren’t scary, like denominators
Make this one easy to solve
Your turn

x
3
1

2
4
1 3
x 
4 2
1 6
x 
4 4
How do I “undo”
subtraction?
Oh no! A fraction…. Are we scared?
NO… fractions aren’t scary, like denominators
Make this one easy to solve
Your turn

x
3
1

2
4
1 3
x 
4 2
1 6
x 
4 4
5
x
4
How do I “undo”
subtraction?
Oh no! A fraction…. Are we scared?
NO… fractions aren’t scary, like denominators
Make this one easy to solve
Your turn
How do I “undo”
subtraction?

x
3
1

2
4
1 3
x 
4 2
1 6
x 
4 4
5
x
4
Oh no! A fraction…. Are we scared?
NO… fractions aren’t scary, like denominators
Make this one easy to solve
CHECK:
5 3
1
 
4 2
4
5 6
1
 
4 4
4
Homework

Page 15