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# 6-2 Solving Two-Step Equations

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by

## Susan Bryan

on 27 January 2016

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#### Transcript of 6-2 Solving Two-Step Equations

Solving Two-Step Equations
Let's Review One-Step Equations:
Ogres and Two-Step Equations
Two-Step Equation
HINT: Start from the
OUTSIDE
layer

Example: 5
X
- 6 = 9

Layer 1:

Layer 2:
Divide both sides by 5
Warm-Up!
Y - 5 = 2
Finish the phrase:
Ogres are like onions, and two-step equations, they all have . . .
LAYERS!
5X + 3 = 8
Example 1 :
Example 2 :
5X - 6 = 9

+6 +6
5X = 15
5 5
X = 3
-3 + 2W = 11
-10 = 6 + 4X
Work this problem and bring it to class:
Name:
4Y - 9 = 15
Two-Step Equations
Definition:
An equation that needs
two steps
to solve

Outside Layer?
5X - 6 = 9
How do you get to the center of an onion?
How do you isolate the variable?
Y - 5 = 2

+5 +5

Y = 7
More Review of One-Step Equations:
Y = 2
5
3x = 12
A.
B.
y = 2
5
y = 5 (2) = 10
3x = 12
A.
B.
3x = 12 = 4
3
3
y = 2
5
(5)
(5)
-3 + 2W = 11
The outside layer is the -3.
+3
Do the opposite to both sides.
+3
2W = 14
What operation is 2 doing to W? (add, subtract, multiply, or divide)
Do the opposite to both sides.
2
2
W = 7
Simplify
-10 = 6 + 4X
The outside layer is the 6. (work on the side the variable is on.)
Do the opposite to both sides.
-6
-6
-16 = 4x
What operation is 4 doing to X? (add, subtract, multiply, or divide)
Do the opposite to both sides.
4
4
Simplify.
-4 = X

http://bcontext.com//bfile/player/dlqdr/?auth=N3PJ3MTJLXZZF5JEJCLM9S8HK3RAU10BLNPOKNLP3YZUOR8YHX

Another Way of Looking At It
In the morning you put on socks first, then your shoes.
Opposite order, opposite action.
Put On - Socks
Put On - Shoes
Take Off - Shoes
Take Off - Socks

1.
1.
2.
2.
Order of Operations is like the Shoes and Socks
2x + 3 = 15
Step 1
How do we make "x" look like "2x + 3" using order of operations?
First we multiply by 2. (x becomes 2x)
Then we add 3. (2x becomes 2x + 3)

Step 2
Solve the problem by working "backwards"

Subtract 3
Divide by 2
2x + 3 = 15
- 3 -3
2x = 12
2 2
x = 6
G G
E E
M M
D D
A A
S S
do
undo
Opposite order
Opposite operation
Do
Undo
2h + 9 = 21
-9 -9
2h = 12

2h = 12
2 2

h = 6
Step 1: 9 was added to 2h so we subtract 9 from BOTH sides
Step 2: h was multiplied by 2 so we divide BOTH sides by 2
We are trying to find x.
What happened to x? It was multiplied by 5. Then 6 was subtracted. 6 is the outside layer
5 is an inside layer because it was last.
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