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Chapter 3: Problem 1

Simplify each expression by combining like terms. $$ 3 x+5 x $$

Short Answer

Expert verified
The simplified expression is \(8x\).

Step by step solution

01

Identify like terms

In the expression \(3x + 5x\), both terms contain the same variable, \(x\). Thus, they are like terms that can be added together.
02

Combine the coefficients

Add the coefficients of the like terms together. The coefficients are 3 and 5. So calculate \(3 + 5\).
03

Write the simplified expression

The sum of the coefficients is 8. So, the expression simplifies to \(8x\).

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is a key concept in prealgebra. The goal of simplification is to make the expression as straightforward as possible. When you simplify, you're looking to combine and reduce terms whenever possible.
To simplify an expression, follow these steps:
  • Identify all like terms in the expression.
  • Combine these like terms by adding or subtracting them.
  • Repeat the process until you can't simplify the expression further.
Once fully simplified, the expression is easier and more efficient to work with.
Combining Like Terms
Combining like terms is an essential process in simplifying expressions. Like terms have the same variable parts, meaning both the variable and the exponent, if any, match.
For example:
  • In the expression \(3x + 5x\), both terms are like terms because they have the same variable \(x\).
  • This means you can combine them by adding their coefficients: \(3 + 5 = 8\).
  • The expression therefore simplifies to \(8x\).
Always look for terms with the same variables and combine them to simplify the expression further.
Coefficients
Coefficients are the numbers that multiply the variable part of a term. They play a crucial role when you're simplifying expressions because they're what you actually add or subtract to combine like terms.
In the expression \(3x + 5x\):
  • The coefficient of the first term is 3.
  • The coefficient of the second term is 5.
  • When combining these like terms, you're essentially calculating the sum of the coefficients, which is \(3 + 5 = 8\).
  • This means the simplified expression is \(8x\).
Understanding coefficients makes it easier to perform operations on algebraic expressions.
Variable Terms
Variable terms are parts of an expression that include variables, such as \(x\) or \(y\). The variable part of these terms can change depending on the value substituted for the variable.
With variable terms, pay attention to:
  • The variable and its power (exponent), if any.
  • All terms with the exact same variable and exponent are like terms and can be combined.
  • For example, in \(3x + 5x\), the variable is \(x\) and the power is 1, making them like terms.
  • Thus, you can simplify the expression to \(8x\).
Being familiar with variable terms helps you organize and simplify complex algebraic expressions.

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