Problem 80 Combine like terms. $$ 16 r+... [FREE SOLUTION]

Chapter 15: Problem 80

Combine like terms. $$ 16 r+(-7 r)+3 s $$

Short Answer

Expert verified

9r + 3s

Step by step solution

Identify the Like Terms

Look at the expression: \[16r + (-7r) + 3s\]Identify terms that have the same variable. The terms 16r and -7r both have the variable 'r'.

Combine the Like Terms

Add the coefficients of the like terms you have identified. For 16r and -7r, combine them by adding the coefficients: \[16 + (-7) = 9\]So, 16r + (-7r) simplifies to 9r.

Rewrite the Expression

Now, rewrite the expression with the combined like terms and any remaining terms: \[9r + 3s\]

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Key Concepts

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

like terms

Understanding like terms is essential when working with algebraic expressions.
Like terms are terms in an expression that have the same variable raised to the same power.
For example, in the expression given, we have 16r + (-7r) + 3s, The terms 16r and -7r are like terms because they both contain the variable r and are raised to the same power (1).
However, 3s is not a like term with 16r or -7r because it has a different variable (s).
Identifying like terms helps to simplify expressions by combining them efficiently.

coefficients

Coefficients are the numerical part of terms that include a variable.
In the expression a r, the coefficient is a.
For our specific example 16r + (-7r) + 3s, The coefficients are 16, -7, and 3.
When combining like terms, only the coefficients change while the variable part remains the same.
So, adding the coefficients of 16r and -7r would be done as follows: combining 16 and -7 yields 9.
This simplifies 16r + (-7r) to 9r.
The variable r stays the same in the simplified term.

simplifying expressions

Simplifying expressions means making them as simple as possible by combining like terms and performing arithmetic operations.
Here are the steps we follow to simplify an expression:

Identify like terms.
Combine the coefficients of like terms.
Rewrite the expression with the combined terms.

Using the given problem as an example:
Expression: 16r + (-7r) + 3sStep 1: Identify like terms: 16r and -7r are like terms, while 3s is not.
Step 2: Combine like terms: 16 + (-7) = 9. So, 16r + (-7r) simplifies to 9r.
Step 3: Rewrite the expression: 9r + 3s.
Simplifying expressions helps make the expression easier to work with, especially for further mathematical operations or solving equations.

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91影视

Combine like terms. $$ 16 r+(-7 r)+3 s $$

Short Answer

Step by step solution

Identify the Like Terms

Combine the Like Terms

Rewrite the Expression

Key Concepts

like terms

coefficients

simplifying expressions

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