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Chapter 5: Problem 5

Add $$ (3 x+2)+(x+7) $$

Short Answer

Expert verified
4x + 9

Step by step solution

01

Identify Like Terms

Separate the expression into like terms. Like terms are terms that contain the same variable raised to the same power. In this case, the like terms are the ones with the variable x and the constant terms (without any variable).
02

Combine Coefficients of x

Add the coefficients of the like terms with the variable x. For the expression (3x + 2) + (x + 7), the coefficients of x are 3 and 1. Adding them gives 3x + x = (3 + 1)x = 4x.
03

Combine Constant Terms

Add the constant terms from the expressions. For the terms 2 and 7, adding them gives 2 + 7 = 9.
04

Write the Final Expression

Combine the results from step 2 and step 3 to get the final simplified expression. Therefore, (3x + 2) + (x + 7) = 4x + 9.

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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 key in polynomial addition.
Like terms are terms that have the same variable and the same power.
For example, in the expression \((3x+2)+(x+7)\), we have:
- Like terms with the variable\(x\): 3x and x
- Constant terms (without any variable): 2 and 7.
Combining Coefficients
To simplify polynomial expressions, you need to combine the coefficients of the like terms.
Coefficients are the numerical parts of terms.
For the expression \((3x + 2) + (x + 7)\):
  • The coefficients of the x terms are 3 and 1 (since x is the same as 1x).
  • Add these coefficients: 3 + 1 = 4.
    • - This gives us 4x after combining the x terms.
Constant Terms
Constant terms are just numbers without variables.
This makes them easier to identify and combine.
For instance, in the expression \((3x + 2) + (x + 7)\):
    - We have constant terms 2 and 7.
  • Add them together: 2 + 7 = 9.

    • So, combining the constant terms gives us 9.

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