Problem 75 Clear parentheses and combine li... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 75

Clear parentheses and combine like terms. $$-3(2 x+1)-13$$

Short Answer

Expert verified

-6x - 16

Step by step solution

- Distribute the -3

Start by distributing the $-3$ to both terms inside the parentheses. This means multiplying $-3$ by $2x$ and $-3$ by $1$.

- Compute the Distributive Step

Perform the multiplication: $-3 \times 2x = -6x$ and $-3 \times 1 = -3$. Combine these results to get $-6x - 3$.

- Combine Like Terms

Now include the term $-13$ from the original equation. Combine it with $-3$ to get the final simplified expression: $-6x - 3 - 13 = -6x - 16$.

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Key Concepts

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

Combining Like Terms

When working with algebraic expressions, it's essential to recognize and combine like terms. Like terms are terms that have the same variable raised to the same power. For example, in the expression $3x + 5x$, both terms are like terms because they both contain the variable $x$. To combine them, simply add their coefficients: $3x + 5x = 8x$.
It鈥檚 also important to manage constants separately. If an expression has multiple constants, such as $-3 - 13$, combine them by performing the arithmetic operation: $-3 - 13 = -16$.
By combining like terms, the expression often becomes much simpler and more manageable.

Simplifying Expressions

Simplifying expressions involves two main steps: using the distributive property and combining like terms.
In the given exercise, the first step is to clear the parentheses by distributing the $-3$ across the terms inside the parentheses. This means multiplying $-3$ by $2x$ and by $1$, which gives $-6x - 3$.
After distribution, the next step is to simplify the expression by combining any like terms. In this exercise, we combine $-3$ and $-13$ to get $-16$. Thus, the simplified expression becomes $-6x - 16$.
These steps ensure that the expression is in its simplest form, making further operations easier.

Prealgebra Concepts

Prealgebra lays the foundation for higher-level math by introducing basic arithmetic and simple algebraic concepts. Key concepts include:

The Distributive Property: This property allows you to distribute a multiplier across terms inside parentheses, such as $a(b + c) = ab + ac$.
Combining Like Terms: Streamlining expressions by adding or subtracting coefficients of the same variable.
Simplifying Expressions: Breaking down complex expressions to their simplest form for easier computation.

Understanding these concepts fundamentally helps in solving more complex algebraic equations and paves the way for advanced math topics.

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91影视

Clear parentheses and combine like terms. $$-3(2 x+1)-13$$

Short Answer

Step by step solution

- Distribute the -3

- Compute the Distributive Step

- Combine Like Terms

Key Concepts

Combining Like Terms

Simplifying Expressions

Prealgebra Concepts

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