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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.

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Combining like terms
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 you answers on the last slide of the lesson.

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 you answers on the last slide of the lesson.

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 you answers on the last slide of the lesson.

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 you answers on the last slide of the lesson.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: you answers on the last slide of the lesson.

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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