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Chapter 15: Problem 76

Combine like terms. $$ 4 x+3 x $$

Short Answer

Expert verified
7x

Step by step solution

01

Identify Like Terms

Identify the like terms in the expression. Here, both terms, 4x and 3x, are like terms because they have the same variable part: 'x'.
02

Combine the Coefficients

Add the coefficients of the like terms together. The coefficients are 4 and 3. So, combine them: 4 + 3 = 7.
03

Write the Combined Term

Attach the variable to the combined coefficient. Therefore, 4x + 3x = 7x.

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Key Concepts

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

Coefficients
In an algebraic expression, the coefficient is the numerical part of a term that is multiplied by the variable. In the given exercise, the terms are 4x and 3x. The numbers 4 and 3 are the coefficients. Coefficients can be positive or negative and are crucial in determining how much of the variable is present in each term.
For example, in the term 4x, 4 is telling us that we have four units of x:
  • 4x: 4 is the coefficient
  • 3x: 3 is the coefficient

When combining like terms, it's important to focus on the coefficients and add them together while keeping the variable part unchanged.
Like Terms
Like terms are terms within an algebraic expression that have the exact same variable part. In our exercise, 4x and 3x are like terms because they both include the variable 'x'.
Understanding like terms:
  • Like terms must have the same variable and the same exponent. For instance, 4x2 and 3x2 are like terms, but 4x and 3x2 are not.
  • Like terms can be combined by adding or subtracting the coefficients, but the variable part remains unchanged.

Combining the like terms helps to simplify the expression, making further calculations easier. In the solution, we identified and added 4x and 3x to get 7x.
Variables
Variables are symbols used to represent unknown values or quantities in an expression or equation. Common variables include letters like x, y, or z.
In our exercise, the variable 'x' is the common element in both terms:
  • Variables can have different values depending on the context of the problem.
  • They are essential for forming equations and expressions that model real-world problems.

The variable part does not change during the process of combining like terms. When we combined 4x and 3x, 'x' remained the same, and only the coefficients were added together, resulting in 7x.

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