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Chapter 15: Problem 79

Combine like terms. $$ -6 x+7+9 x $$

Short Answer

Expert verified
3x + 7

Step by step solution

01

- Identify like terms

Like terms are those terms that contain the same variable raised to the same power. In the expression ewline -6x + 7 + 9xewline, the like terms are ewline -6x and 9xewline.
02

- Combine the like terms

Add the coefficients of the like terms:ewline (-6 + 9)x = 3xewline. The constant term, 7, remains unchanged.
03

- Write the simplified expression

The simplified expression is the result from adding the like terms:ewline 3x + 7.

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Key Concepts

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

Identifying Like Terms
Like terms are terms within an expression that have the same variables raised to the same power. For example, in the expression ewline -6x + 7 + 9x ewline, the terms ewline -6x ewline and ewline 9x ewline are like terms because they both contain the same variable, ewline x, ewline raised to the same power, which is 1.
Identifying like terms is the first step in simplifying expressions. It helps you to combine these terms more efficiently. Here are some tips to identify like terms:
  • Look for the same variable in each term.
  • Ensure the variables have the same exponent.
  • Constant terms (numbers without variables) are also considered as like terms but are only combinable with other constants.
Coefficients
Coefficients are the numerical part of terms that contain variables. In the term ewline -6x, ewline the coefficient is ewline -6. ewline Likewise, in ewline 9x, ewline the coefficient is ewline 9.
When combining like terms, we add or subtract their coefficients, while keeping the variable part unchanged.
For instance, in the step-by-step solution given:
-6x + 9x ewlineewline is simplified by combining the coefficients -6 and 9.
This gives:ewline (-6 + 9)x = 3x.
By focusing on the coefficients, we can quickly simplify expressions.
Simplifying Expressions
Simplifying expressions involves combining like terms and reducing the expression to its simplest form.
After identifying like terms and adding their coefficients, the expression becomes more manageable.
For the given exercise: The initial expression: ewline -6x + 7 + 9x ewlineewline was simplified to: ewline 3x + 7.
Here are the steps for simplifying any algebraic expression:
  • Identify like terms.
  • Combine the coefficients of the like terms.
  • Keep the constant terms separate and add them at the end.
Simplifying expressions makes them easier to handle and prepares them for solving equations or further operations.

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