Solving Two Step Equations

1
Solving Two Step Equations

• Students will solve two-step equations using
  inverse operations.

3a 5 11
-3n 16 - 2
-2x 8 16
2y ( - 3 ) - 15
2
Review One-step Equations
m 9 3
f 3 -5
- 9 - 9
3 3
m -6
f -2
check -2 3 ?
check -6 9 ?
3 3 ?
-5 -5 ?
(-5) (-5)
3a -18
3 3
x 10
a -6
Check
Check 3 (-6) ?
-18 -18 ?
-2 -2 ?
3
Two-Step Equations

• It takes two steps to solve an equation that has
  more than one operation.
• Use PEMDAS backwards
• Simplify by using the addition or subtraction
  property of equality. (use the inverse of
  addition or subtraction)
• Simplify further by using the multiplication or
  division property of equality. (use the inverse
  of multiplication or division)

4
2-step Equation w/ Algebra Tiles
x 1
3x 2 11


Subtract 2 from each side of the equation.

Divide into equal groups.

x 3
5
Example 1

• 2x 15 5

15 15 Addition Property of Equality
2x 20
2 2 Division Property of Equality
x 10
CHECK YOUR WORK
2 ( 10 ) 15 ? 20 15 5 5
?
6
Example 2

• 11n 1 67

1 1 Subtraction Property of Equality
11n 66
11 11 Division Property of Equality
n 6
CHECK YOUR WORK
11 ( 6 ) 1 ? 66 1 67 67
?
7
Example 3

• -2y 4 8

4 4 Subtraction Property of Equality
-2y 4
-2 -2 Division Property of Equality
y -2
CHECK YOUR WORK
-2 (-2 ) 4 ? 4 4 8
8
?
8
Example 4

• 5x 2 3

2 2 Addition Property of Equality
5x 5
5 5 Division Property of Equality
x 1
CHECK YOUR WORK
5 ( 1 ) 2 ? 5 2 3
3
?
9
Example 5
x 5
9 -2
9 9 Addition Property of Equation
x 5
( 5 ) ( 5 ) Multiplication
Property of Equation
7
Check your answer
x 35
35 5
9 ?
7 9
?
-2 -2
10
Word Problem 1

• Bobby bought 3 T-shirts at the mall and a pair of
  pants for 16 at the clothing store. All
  together he spent 28 for the clothes. How much
  was each shirt?

28
Let T the price of each T-shirt.
16
3T
16 16 Subtraction Property of Equations
3T 12
3 3 Division Property of Equations
T 4
Each T-shirt cost 4 .
11
Word Problem 2

• Diane sold 9 decorated flowers that cost the same
  amount each plus a dozen roses for 28. All
  together she sold 73 in flowers. How much was
  each decorated flower?

73
Let F the price of each decorated flower.
28
9F
28 28 Subtraction Property of Equations
9F 45
9 9 Division Property of Equations
F 5
The decorated flowers were 5.00 each.
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Solve for x with variables
ax b y
b b Subtract b from both sides.
y b
ax
Since y and b are not like terms, we cannot
combine them.
a a
y b a
Divide both sides of the equation by a.
x
y a
b a
OR
x
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Summary
Remember, use inverse operations to solve
equations. Work in reverse order of operations.
STOP