Problem 70 - Elementary and Intermediate Algebra

Question

Combine like terms. \(-3 x+8 x\)

Step-by-Step Solution

Answer

The simplified expression is 5x.

Step 1: Identify the like terms

Determine the terms with the same variable. Here, -3x and 8x both have the variable x.

Step 2: Combine the coefficients

Add the coefficients of the like terms. The coefficients are -3 and 8. So, -3 + 8.

Step 3: Simplify the expression

Perform the arithmetic operation: -3 + 8 = 5. Attach the result to the variable, resulting in 5x.

Key Concepts

algebraic expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. They are essential in forming equations and inequalities.
In \(-3x + 8x\), the individual components \-3x\ and \8x\ are called terms. Terms in algebraic expressions can include:

• Constants: Numbers on their own (e.g., 5, -2).
• Variables: Symbols representing unknown values (e.g., x, y).
• Coefficients: Numbers multiplying the variables (e.g., -3 in -3x).

Understanding the parts that make up algebraic expressions helps in solving and simplifying them.

coefficients

Coefficients are the numerical part of the terms in an algebraic expression and are used to multiply the variables. For example, in \(-3x + 8x\), the coefficients are \-3\ and \8\.
When combining like terms, it's crucial to focus on the coefficients:

• Identify the terms with the same variable.
• Add or subtract the coefficients while keeping the variable unchanged.

In the given problem, \(-3x\ and \8x\) can be combined because they have the same variable, \x\:
\(-3 + 8 = 5\), so the simplified expression is \5x\.

simplifying expressions

Simplifying expressions involves combining like terms to make the expression easier to work with. Like terms are terms in an algebraic expression that have the same variables raised to the same power.
Here’s a quick recap of how to simplify the given problem \(-3x + 8x\):

• Identify the like terms: Both terms have the variable \x\.
• Combine the coefficients: \-3 + 8 = 5\.
• Attach the result to the variable: The simplified expression is \5x\.

Simplifying expressions not only makes them easier to understand but also sets the groundwork for solving more complex algebraic equations.