Problem 70 Simplify each expression. $$ ... [FREE SOLUTION]

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Chapter 1: Problem 70

Simplify each expression. $$ 5 x-(2 x-7) $$

Short Answer

Expert verified

3x + 7

Step by step solution

- Distribute the Negative Sign

First, distribute the negative sign across the parentheses: $ 5x - (2x - 7) = 5x - 2x + 7 $

- Combine Like Terms

Next, combine the like terms: $ 5x - 2x = 3x $. So we have: $ 3x + 7 $

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Key Concepts

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

distributive property

When simplifying an algebraic expression, the distributive property is an essential tool. It helps to eliminate parentheses by distributing whatever is outside the parentheses to each term inside. The distributive property states that for any numbers and variables, $a(b + c) = ab + ac$. In the case of our example, we have to distribute the negative sign through the terms inside the parentheses, converting $5x - (2x - 7)$ to \[5x - 2x + 7\]. Here, we distribute the negative sign to both $2x$ and $-7$. This makes the expression easier to manage, ready for the next step, combining like terms.

combining like terms

After distribution, the next vital step in simplifying an expression is combining like terms. Like terms are terms that have the same variable raised to the same power. In our problem, after applying the distributive property, we get \[5x - 2x + 7\]. The terms $5x$ and $2x$ are like terms because they both have the same variable $x$. We combine them by performing the operation shown: \[5x - 2x = 3x\]. The expression then becomes \3x + 7\. By isolating and combining like terms, we reduced the complexity of the expression, making it much easier to interpret and use.

algebraic simplification

Algebraic simplification is the process of making an algebraic expression as simple as possible. This involves using the distributive property and combining like terms to reduce the number of terms and simplify the expression. In our problem, we start with \[5x - (2x - 7)\]. First, we apply the distributive property: \[5x - 2x + 7\]. Next, we combine like terms: \[5x - 2x = 3x\], so the expression simplifies to \[3x + 7\]. The goal of algebraic simplification is to make the expression more manageable and to find a form that is easier to work with in solving equations or performing further operations.

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91影视

Simplify each expression. $$ 5 x-(2 x-7) $$

Short Answer

Step by step solution

- Distribute the Negative Sign

- Combine Like Terms

Key Concepts

distributive property

combining like terms

algebraic simplification

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