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Chapter 1: Problem 38

Simplify each expression. $$ 5 m+2 m $$

Short Answer

Expert verified
7m

Step by step solution

01

Identify like terms

In the expression, identify terms that can be combined. Here, both terms, 5m and 2m, have the variable 'm' and are considered like terms.
02

Add the coefficients

Add the coefficients (numeric parts) of the like terms. So, add 5 and 2.
03

Combine the terms

Combining the coefficients gives you 7. Therefore, the simplified expression is 7m.

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Key Concepts

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

like terms
In algebra, the term 'like terms' is crucial. It refers to terms that have identical variable parts. For example, in the expression \(5m + 2m\), both terms are 'like terms' because they each have the variable 'm'. Remember:
  • The variable part must be the same for terms to be considered like terms.
  • Only like terms can be combined or simplified.
So, it's essential to first identify like terms before attempting to simplify an expression.
coefficients
The coefficient is the numerical part of a term that multiplies its variable. In the expression \(5m + 2m\), the numbers 5 and 2 are the coefficients. Key points to note:
  • It's the number directly in front of the variable.
  • Each term must be noted separately along with its coefficient.
  • When simplifying, only the coefficients are added or subtracted.
Making sure you understand coefficients will help you correctly simplify algebraic expressions.
combining terms
Combining terms is the final step when simplifying algebraic expressions. After identifying like terms and their coefficients, you add or subtract these coefficients. Following the steps:
  • Identify like terms.
  • Look at their coefficients.
  • Add or subtract the coefficients, keeping the common variable part the same.
For example, combining the terms in \(5m + 2m\): \(5 + 2 = 7\). So, \(5m + 2m\) simplifies to \(7m\). Understanding how to combine like terms will make simplifying expressions much easier and more intuitive.

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