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Chapter 1: Problem 72

Combine like terms. \(2 m+(-7 m)\)

Short Answer

Expert verified
-5m

Step by step solution

01

Identify the Like Terms

Look at the terms in the expression and identify the like terms. Here, both terms, 2m and -7m, have the variable m.
02

Combine the Coefficients

Add the coefficients (numbers in front of the variables) of the like terms together: 2 + (-7).
03

Simplify the Expression

Perform the addition: 2 + (-7) = -5. Therefore, the expression simplifies to -5m.

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Key Concepts

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

algebraic expressions
An algebraic expression is a mathematical phrase that can contain numbers, variables (like m), and operations (such as addition and subtraction). In the exercise, the algebraic expression is composed of two terms: 2m and -7m. These terms include a coefficient (the number) and a variable (m). Algebraic expressions do not include an equality sign (=); they represent quantities that can be simplified or evaluated.
Understanding algebraic expressions is crucial because they form the foundation for solving equations and understanding algebra.
coefficients
Coefficients are the numbers in front of the variables in an algebraic expression. In the given problem, the coefficients are 2 and -7 in the terms 2m and -7m, respectively. Coefficients tell us how many times the variable is being multiplied. For instance, the coefficient 2 in 2m means that m is being multiplied by 2.
When combining like terms, it is vital to focus on the coefficients. In our exercise, we added 2 and -7 to get -5. This is the combined coefficient that simplifies our expression.
simplifying expressions
Simplifying expressions involves combining like terms to make the expression as concise as possible. Like terms are terms that have the same variable raised to the same power.
In our given exercise, both terms (2m and -7m) are like terms because they both contain the variable 'm'. To simplify an expression:
  • Identify the like terms
  • Combine their coefficients
  • Return the simplified term
The simplified expression from 2m + (-7m) is -5m, making the expression cleaner and easier to work with.

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