Problem 82 Remove parentheses and simplify.... [FREE SOLUTION]

Chapter 15: Problem 82

Remove parentheses and simplify. $$ 4 r-(3 r+5) $$

Short Answer

Expert verified

\[ r - 5 \]

Step by step solution

Distribute the Negative Sign

Distribute the negative sign in front of the parentheses to each term inside. This changes the signs of the terms inside the parentheses. Convert $ -(3r+5) $ to $ -3r - 5 $. So we then have: \[ 4r - (3r + 5) = 4r - 3r -5 \].

Combine Like Terms

Combine the terms with the variable $ r $. In this case, combine $ 4r - 3r $ which results in $ r $. We now have \[ r - 5 \].

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Key Concepts

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

Distributing Negative Signs

In algebra, distributing the negative sign is important when simplifying expressions involving parentheses. Negative signs can change the sign of each term within the parentheses, ensuring the equation remains balanced.
For example: let's start with the expression: 4r - (3r + 5).
Here, the negative sign in front of the parentheses applies to all terms inside the parentheses. This turns -(3r + 5) into -3r - 5.
Thus the expression 4r - (3r + 5) transforms into 4r - 3r - 5.

To properly distribute:

Identify the negative sign in front of the parentheses.
Convert each term inside the parentheses by changing their signs.

Combining Like Terms

Combining like terms helps in simplifying algebraic expressions neatly and correctly.
Like terms are terms that have identical variable parts.
For example, in the expression: 4r - 3r - 5, 4r and 3r are like terms because they both have the variable r.
So, to simplify, combine these like terms together: 4r - 3r = r.
After combining, the equation becomes much simpler: r - 5. To combine like terms:

Identify terms with the same variable.
Add or subtract their coefficients while keeping the variable part unchanged.

Parentheses Removal in Algebra

Removing parentheses is a crucial part of simplifying algebraic expressions. This process often involves distributing any signs or coefficients outside the parentheses.
For the expression: 4r - (3r + 5), we first remove the parentheses by distributing the negative sign: this leaves us with: 4r - 3r - 5.

Next step is simplifying by combining like terms to reach the final expression: r - 5.
To effectively remove parentheses:

Distribute any constants or signs in front of the parentheses to each term inside.
Combine any resulting like terms to simplify the expression fully.

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91影视

Remove parentheses and simplify. $$ 4 r-(3 r+5) $$

Short Answer

Step by step solution

Distribute the Negative Sign

Combine Like Terms

Key Concepts

Distributing Negative Signs

Combining Like Terms

Parentheses Removal in Algebra

One App. One Place for Learning.

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