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### Solving Multi-Step Equations

Lesson 2-3

Combining Like Terms:

A. 5 = 5m – 23 + 2m Original Equation

5m – 23 + 2m = 5 Symmetric Property

5m + 2m + – 23 = 5 Commutative Property

7m + – 23 = 5 Combine Like Terms

7m + – 23 + 23 = 5 + 23 Undo subtraction by adding

7m = 28 Simplify (substitution property)

Undo multiplication by dividing

m = 4 Simplify (substitution property)

B.Martha takes her niece and nephew to a concert. She buys T-shirts and bumper stickers for them. The bumper stickers cost $1 each. Martha’s niece wants 1 shirt and 4 bumper stickers, and her nephew wants 2 shirts, but no bumper stickers. If Martha’s total $67, what is the cost of one shirt?

Let _______ = cost of one shirt

c

_________________________ Cost of 1 shirt + 4 bumper stickers + cost of 2 shirts = total spent

___________________________ Commutative property

___________________________ Combine Like Terms

___________________________ Undo the addition

___________________________ Simplify (Substitution property)

___________________________ Undo the multiplication

___________________________ Simplify (Substitution property)

c + 4(1) + 2c = 67

c + 2c + 4 = 67

3c+ 4 = 67

3c + 4 – 4 = 67 – 4

3c = 63

c = 21

Complete the practice problems in your notes. You can check you answers on the last slide of the lesson.

Solving an Equation Using the Distributive Property

C. –8 (2x – 1) = 36

–8 (2x + –1) = 36

Rewrite the subtraction as adding the opposite.

–16x + 8 = 36

Use the distributive property.

–16x + 8 – 8 = 36 – 8

Subtract 8 from each side (undo the addition.)

–16x = 28

Simplify

Divide each side by -16 (undo the multiplication)

Simplify

Solving an Equation that Contains Fractions

D. Method 1:

Get a common denominator

12 is the LCD for 4 and 3

Remember only subtract numerators.

Multiply by the reciprocal.

Multiply straight across (10 is a numerator).

x = 24

Simplify

Solving an Equation that Contains Fractions

D1. Method 2: Clear the fractions from the equation

Because 12 is the LCD for 4 and 3, multiply both sides by 12. This eliminates fractions.

Distributive property

9x – 4x = 120

5x = 120

Combine Like Terms

Divide by 5 (undo the multiplication.)

x = 24

Simplify

Solving an Equation that Contains Decimals

3.5 – 0.02x = 1.24

_____________________________ Multiply each side by 102 (because there are 2

places behind the decimal)

_____________________________ Distributive Property

_____________________________ Subtract from each side.

_____________________________ Simplify

_____________________________ Divide each side by – 2

_____________________________ Simplify

(100) (3.5 – 0.02x) = 1.24 (100)

350 – 2x = 124

350 – 350 – 2x = 124 – 350

– 2x = – 226

x = 113

Solutions to practice problems:

m = 6

y = 3

One pack of strings is $14.

You earn $8 per hour.

x = 6

x =

7. b =

8. m =

x = 12.55

x = 2

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