Problem 82 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 1: Problem 82

Simplify each expression. $$ (3 x+5)+(4 x+12) $$

Short Answer

Expert verified

7x + 17

Step by step solution

- Identify Like Terms

The expression to simplify is (3x + 5) + (4x + 12). Identify the like terms in the expression. In this case, the like terms are the terms with the variable x (3x and 4x) and the constant terms (5 and 12).

- Combine Like Terms

Combine the like terms. Add the coefficients of the terms with x: 3x + 4x = 7x. Next, add the constant terms: 5 + 12 = 17.

- Write the Simplified Expression

After combining the like terms, write the simplified expression: 7x + 17.

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Key Concepts

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

Understanding Like Terms

Like terms are the foundation of simplifying algebraic expressions. They are terms in an expression that have the same variables raised to the same power. For example, in the expression (3x + 5) + (4x + 12), the like terms are 3x and 4x because they both have the variable x. Similarly, 5 and 12 are like terms because they are both constants without any variables.
Combining like terms makes an expression easier to work with and understand.
Understanding the basics of like terms will help you simplify almost any algebraic expression.

Combining Coefficients

Once you've identified the like terms, the next step is to combine their coefficients. The coefficient is the numerical part of a term that includes a variable. For instance, in 3x, '3' is the coefficient. Similarly, in 4x, '4' is the coefficient. To combine the coefficients:
鈥� Add the coefficients of the like terms with variables. In our example: $3x + 4x = 7x $.
鈥� Add the constant terms. For our constants: $ 5 + 12 = 17 $.
Combining coefficients helps in simplifying the expression step by step.

Simplification Steps

When simplifying algebraic expressions, follow a structured approach:
1. **Identify Like Terms**: Recognize the terms in the expression that have the same variables and constants.
In $ (3x + 5) + (4x + 12) $, the like terms are $ 3x, 4x $ and the constants are $ 5, 12. $
2. **Combine Like Terms**: Add the coefficients of the like terms. For the variables: $ 3x + 4x = 7x $.
Add the constants: $ 5 + 12 = 17 $.
3. **Write the Simplified Expression**: Put it all together. The simplified form of the original expression (3x + 5) + (4x + 12) is $ 7x + 17 $.
Following these steps ensures that you can simplify any algebraic expression correctly and confidently.

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91影视

Simplify each expression. $$ (3 x+5)+(4 x+12) $$

Short Answer

Step by step solution

- Identify Like Terms

- Combine Like Terms

- Write the Simplified Expression

Key Concepts

Understanding Like Terms

Combining Coefficients

Simplification Steps

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