Problem 113 Combine like terms. $$ 7 a-1... [FREE SOLUTION]

Chapter 1: Problem 113

Combine like terms. $$ 7 a-12 a+4 $$

Short Answer

Expert verified

-5a + 4

Step by step solution

Identify like terms

Look at the expression: 7a - 12a + 4. Identify the terms that have the same variable. In this case, the terms 7a and -12a both have the variable 'a'.

Combine like terms

Combine the coefficients of the like terms: 7a and -12a. To do this, add them together: 7 - 12 = -5. So, 7a - 12a simplifies to -5a.

Simplify the expression

Now, rewrite the expression combining the like terms and maintaining the constant: The simplified form is -5a + 4.

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Key Concepts

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

Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and operations. They allow us to represent mathematical relationships in a general form. In the exercise, the expression 7a - 12a + 4 is an example of an algebraic expression. Here, 'a' is a variable, and 7 and -12 are coefficients. The term '4' is a constant since it does not have a variable attached.
Understanding the structure of algebraic expressions helps in performing operations such as addition, subtraction, and simplification. By recognizing different parts of the expression, you can easily manipulate and combine terms correctly.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form. This often includes combining like terms, which makes the expression easier to understand and work with.
To simplify 7a - 12a + 4, we:
1. Identify like terms: In this case, the terms with the variable 'a' are 7a and -12a.
2. Combine like terms: We add their coefficients (7 and -12) to get -5.
3. Rewrite the expression: Combining these terms gives us -5a, and we keep the constant 4. So the simplified expression is -5a + 4.
Simplifying expressions helps in solving equations and understanding relationships between variables more clearly.

Coefficients

Coefficients are the numerical parts of the terms that include variables. They represent the number of times a variable is multiplied. In the exercise, 7 and -12 are coefficients for the variable 'a'.
When combining like terms, we focus on the coefficients. Here's how we do it:
1. Identify terms with the same variable.
2. Add or subtract their coefficients.
3. Combine them into a single term with the same variable.
For example, in 7a - 12a, the coefficients are 7 and -12. Combining these, we get 7 - 12 = -5, so the term simplifies to -5a.
Recognizing and working with coefficients is a key skill in algebra that makes handling expressions straightforward and logical.

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91影视

Combine like terms. $$ 7 a-12 a+4 $$

Short Answer

Step by step solution

Identify like terms

Combine like terms

Simplify the expression

Key Concepts

Algebraic Expressions

Simplifying Expressions

Coefficients

One App. One Place for Learning.

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