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Chapter 1: Problem 94

Simplify each expression. \(-2(3 r-4)-(6-r)+2 r-5\)

Short Answer

Expert verified
-3r - 3

Step by step solution

01

Distribute the -2

Apply the distributive property to the term \(-2(3r - 4)\): \{-2 * 3r + (-2) * (-4) = -6r + 8}.
02

Distribute the negative sign

Apply the distributive property to the term \( -(6 - r) \): \{-6 + r}.
03

Combine like terms

Combine all like terms: \(-6r + 8 - 6 + r + 2r - 5 \). Group the r terms and the constant terms: \{(-6r + r + 2r) + (8 - 6 - 5)}. Simplify the grouped terms: \{-3r - 3}.

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Key Concepts

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

Distributive Property
The distributive property is a fundamental concept in algebra that helps us simplify expressions by distributing or multiplying a single term across terms inside a parenthesis. For example, in the expression \(-2(3r - 4)\), we apply the distributive property by multiplying \-2\ with each term inside the parenthesis. This gives us:
\(-2 * 3r = -6r\) and \(-2 * (-4) = 8\). Combining these results, we get \(-6r + 8\).
Distributing makes larger expressions easier to handle by breaking them down. Remember to keep track of positive and negative signs when distributing terms.
Combining Like Terms
Combining like terms is the process of simplifying an expression by merging terms that have the same variable part. In the expression \(-6r + 8 - 6 + r + 2r - 5\), like terms share the same variable: \r\ terms and constant terms. Let's identify and group them:
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Most popular questions from this chapter

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