Problem 34 Simplify. $$ 3 y-13 y-y+4 y-... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 7: Problem 34

Simplify. $$ 3 y-13 y-y+4 y-2 $$

Short Answer

Expert verified

The simplified expression is $-7y - 2$.

Step by step solution

Identify Like Terms

In the expression $3y - 13y - y + 4y - 2$, identify the terms that contain the variable $y$, which are $3y$, $-13y$, $-y$, and $4y$. The number $-2$ is the constant term.

Combine Like Terms

Add the coefficients of like terms: $3y - 13y - y + 4y = (3 - 13 - 1 + 4)y = -7y$.

Simplify Further

Once the like terms have been combined, you obtain $-7y$. Since there's also a constant, the final simplified form of the expression is $-7y - 2$.

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Key Concepts

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

Understanding Like Terms

In algebra, like terms are terms that have identical variables raised to the same powers. For instance, in the expression $3y - 13y - y + 4y - 2$, the like terms are those that involve the variable $y$: $3y$, $-13y$, $-y$, and $4y$. These terms can be combined because they have the same variable part.

Variable Part: This is the letter or symbol in a term that represents an unknown value, like $y$ in this case.
Coefficient: This is the number located in front of a variable, for example, the number 3 in $3y$.

Like terms make it easier to combine and simplify expressions because they behave in a consistent and predictable way when operations are performed on them.

Exploring Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and arithmetic operations such as addition, subtraction, multiplication, and division. The expression given in the exercise, $3y - 13y - y + 4y - 2$, is a perfect example of an algebraic expression.

Terms in Expressions: Each part of the expression separated by a plus or minus sign is a term. In this case, the terms are $3y$, $-13y$, $-y$, $4y$, and $-2$.
Constants: These are terms without variables, like $-2$.

Understanding algebraic expressions allows you to manipulate and simplify them by using mathematical operations, making them easier to interpret and solve.

Strategy for Combining Like Terms

Combining like terms is an essential step in simplifying algebraic expressions. The goal is to make the expression as simple as possible.
Here鈥檚 how you can think about combining like terms with our given expression, $3y - 13y - y + 4y - 2$:

Identify the Like Terms: First, pick out the terms that involve the same variables, like the $y$ terms.
Add/Subtract the Coefficients: Perform addition or subtraction on their coefficients only. So, compute $3 - 13 - 1 + 4$, which gives $-7$.
Reform the Expression: Attach the resulting coefficient to the variable, giving $-7y$.
Include Constants: Don鈥檛 forget to include any non-variable terms like $-2$ in the final result.

Thus, when you combine like terms, you streamline the expression into a simpler form, $-7y - 2$, which is much easier to work with in further calculations.

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91影视

Simplify. $$ 3 y-13 y-y+4 y-2 $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Simplify Further

Key Concepts

Understanding Like Terms

Exploring Algebraic Expressions

Strategy for Combining Like Terms

One App. One Place for Learning.

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