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3 years ago

Does the order of variables matter when combining like terms in algebra

1 answer:

4 0

Answer: No
The order of variables does not matter when combining like terms in algebra, because of the commutative property.

Explanation:
Consider the addition of two algebraic expressions.
f(x) = x³ - 5x² + 3x - 2
g(x) = 6x³ + 10x² - 7x + 9

Add f(x) and g(x).
f(x) + g(x) = x³ - 5x² + 3x - 2 + (6x³ + 10x² - 7x + 9)
= x³ + 6x³ - 5x² + 10x² + 3x - 7x - 2 + 9
= 7x³ + 5x² - 4x + 7

Now add g(x) and f(x) in order to change the order of variable addition.
g(x) + f(x) = 6x³ + 10x² - 7x + 9 + (x³ - 5x² + 3x - 2)
= 6x³ + x³ + 10x² - 5x² - 7x + 3x + 9 - 2
= 7x³ + 5x² - 4x + 7

The two additions yield the same result, although the order of variable was reversed during the addition.

In general, algebraic operations are commutative.

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Required 1.

Jan 1

Cash $30,000 (debit)

Capital $30,000 (credit)

Jan 2

Rent Expense $2,450 (debit)

Cash $2,450 (credit)

Jan 3

Supplies $2,200 (debit)

Accounts Payable $2,200 (credit)

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Cash $2,000 (debit)

Jan 8

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Supplies $1,100 (credit)

Jan 9

Capital $3,200 (debit)

Cash $3,200 (credit)

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Capital = $ 26,800 (credit)

Rent Expense $2,450 (debit)

Supplies = $ 1,100 (debit)

Accounts Payable = $ 1,350 (credit)

Fees Earned $14,940 (credit)

Automobile Expenses $1,580 (debit)

Miscellaneous expenses $470 (debit)

Salaries Expenses $2,000

Supplies Expense $1,100

Required 3.

Debit Credit

Cash $ 34,390

Capital $ 26,800

Rent Expense $2,450

Supplies $ 1,100

Accounts Payable $ 1,350

Fees Earned $14,940

Automobile Expenses $1,580

Miscellaneous expenses $470

Salaries Expenses $2,000

Supplies Expense $1,100

Totals $43,100 $43,100

Required 4.

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c. Amount of net income for January = $7,340

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Fees Earned $14,940 (credit)

Automobile Expenses $1,580 (debit)

Miscellaneous expenses $470 (debit)

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Less Drawings ($3,200)

Change $4,140

Therefore, Owners Equity Increased by $4,140

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