Problem 69 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 3: Problem 69

Simplify each expression. $$ 5 y-2(y-1)+3 $$

Short Answer

Expert verified

The simplified expression is $3y + 5$.

Step by step solution

Distribute the terms inside the parentheses

First, distribute the -2 inside the parentheses in the expression -2(y - 1). This means you'll multiply -2 by each term inside the parentheses: $-2(y - 1) = -2 imes y + (-2) imes (-1) = -2y + 2$. Now the expression becomes 5y - 2y + 2 + 3.

Combine like terms

Now that the expression 5y - 2y + 2 + 3 is simplified, combine the like terms. The like terms are 5y and -2y, which combine to 5y - 2y = 3y. The constant terms are 2 and 3, which combine to 2 + 3 = 5. Therefore, the simplified expression is 3y + 5.

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Key Concepts

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

Distributing Terms

Distributing terms involves multiplying a number outside the parentheses by each term inside. This is an essential skill in simplifying algebraic expressions, allowing you to eliminate the parentheses step by step. Consider the expression

$-2(y-1)$

To distribute the

$-2$ across the terms in the parentheses, multiply it by each item inside.

This means:

$-2 \times y = -2y$
and $-2 \times (-1) = 2$

By performing these calculations, the expression changes. Understanding how to distribute correctly is crucial as errors during this step can lead to incorrect simplifications later.

Combining Like Terms

Combining like terms means grouping together terms that have similar variables and powers. This step helps in reducing the complexity of an expression, making it easier to interpret or evaluate.In the expression seen earlier,

$5y - 2y + 2 + 3$, we have two types of terms:

Variable terms: $5y$ and $-2y$ both involving the variable $y$.
Constant terms: $2$ and $3$, which do not involve any variables.

Simplifying these terms, we combine the variable terms

$5y - 2y = 3y$,

and the constant terms

$2 + 3 = 5$.

Using this approach ensures that the expression is in its simplest form.

Prealgebra

Prealgebra serves as the foundational stepping stone in the world of mathematics, introducing key concepts that prepare students for more advanced topics. By focusing on basic arithmetic, fractions, and beginning algebraic concepts, prealgebra helps students build a strong mathematical base. One critical part of prealgebra is mastering the skill of simplifying expressions. It involves:

Understanding operations like addition, subtraction, multiplication, and division.
Learning how to manipulate and simplify expressions through distributing terms and combining like terms.

Prealgebra simplifies complex ideas, making them more relatable and less daunting for students. Techniques learned at this stage are crucial for success in subsequent levels of math.

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91影视

Simplify each expression. $$ 5 y-2(y-1)+3 $$

Short Answer

Step by step solution

Distribute the terms inside the parentheses

Combine like terms

Key Concepts

Distributing Terms

Combining Like Terms

Prealgebra

One App. One Place for Learning.

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