Problem 72 Perform the indicated operations... [FREE SOLUTION]

Chapter 8: Problem 72

Perform the indicated operations. \((12+7 y)-(-3+2 y)\)

Short Answer

Expert verified

15 + 5y

Step by step solution

- Distribute the negative sign

First, distribute the negative sign in front of the second group of terms: \(12 + 7y - (-3 + 2y)\), which simplifies to \(12 + 7y + 3 - 2y\). This results from changing the signs of \(-3 + 2y\) to \(+3 - 2y\).

- Combine like terms

Next, combine the like terms. Combine the constants \(12 + 3 \) and the terms with \(y\) \( 7y - 2y\): \(12 + 3 + 7y - 2y\).

- Simplify

Now, simplify the expression: \(12 + 3 = 15\) and \(7y - 2y = 5y\). Therefore, the expression simplifies to \(15 + 5y\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combining Like Terms

In algebra, 'like terms' are terms that contain the same variables raised to the same power. For example, in the expression 12 + 7y - 2y, '7y' and '-2y' are like terms because they both involve the variable 'y'.

When combining like terms:

Add or subtract the numerical coefficients (numbers in front) of the like terms.
Keep the variable part the same - only the coefficients change.

In the given problem, after distributing the negative sign, we have like terms: 7y - 2y. By subtracting the coefficients, 7 - 2, we combine them into a single term, 5y.

Combining like terms helps to simplify expressions, making them easier to work with and understand.

Distributive Property

The distributive property lets you multiply a single term across each term within parentheses. For instance, in the expression 12 + 7y - (-3 + 2y), we distribute the negative sign:

Multiplying -1 by -3 gives us +3.
Multiplying -1 by +2y gives us -2y.

So the expression becomes 12 + 7y + 3 - 2y.

The distributive property helps to break down complex expressions into simpler ones by distributing multipliers or signs across grouped terms.

Simplifying Expressions

Simplifying an algebraic expression means to combine like terms and perform any operations to make the expression as simple as possible. To simplify:

First, distribute any numbers or signs outside parentheses.
Next, combine like terms by adding or subtracting their coefficients.
Finally, perform any additional arithmetic to simplify the constants.

From the exercise:

1. Distribute (remove the parentheses) to get 12 + 7y + 3 - 2y.
2. Combine like terms: Constants (12 + 3) and terms with y (7y - 2y).
3. This results in the simplified expression 15 + 5y.

Simplification makes algebraic expressions more manageable and often allows us to see solutions more clearly.

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91影视

Perform the indicated operations. \((12+7 y)-(-3+2 y)\)

Short Answer

Step by step solution

- Distribute the negative sign

- Combine like terms

- Simplify

Key Concepts

Combining Like Terms

Distributive Property

Simplifying Expressions

One App. One Place for Learning.

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