3x-2 simplify

Daniel Parker

2 min read

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22-02-2025

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The expression "3x - 2" is a simple algebraic expression. Simplifying it means writing it in its most concise form. In this case, it's already in its simplest form! Let's explore why and look at similar examples to solidify understanding.

Understanding the Components

Before we dive into simplification, let's break down the expression:

• 3x: This is a term consisting of a coefficient (3) and a variable (x). The coefficient indicates that the variable 'x' is multiplied by 3.

• -2: This is a constant term, a numerical value without a variable.

Why 3x - 2 is Already Simplified

We can't combine the terms 3x and -2 because they are unlike terms. Unlike terms have different variables or different exponents on the variables. To combine terms, they must be like terms.

Like Terms: These terms have the same variable raised to the same power. For example:

• 5x and 2x are like terms (both have 'x' to the power of 1).
• 4y² and -7y² are like terms (both have 'y' to the power of 2).
• 6 and 10 are like terms (both are constants).

Unlike Terms: These terms have different variables or different powers of the same variable. For example:

• 3x and 2y are unlike terms (different variables).
• 4x² and 7x are unlike terms (different exponents of 'x').
• 5x and 2 are unlike terms (one has a variable, the other is a constant).

Since 3x and -2 are unlike terms, the expression 3x - 2 cannot be simplified further. It's already in its most basic form.

Examples of Simplifying Like Terms

Let's look at examples where we can simplify by combining like terms:

Example 1:

5x + 2x = 7x (Both terms have 'x' to the power of 1).

Example 2:

4y² - 7y² = -3y² (Both terms have 'y' to the power of 2).

Example 3:

6 + 10 - 3 = 13 (All terms are constants).

Example 4: A slightly more complex example:

2x + 5 + 3x - 2 = (2x + 3x) + (5 - 2) = 5x + 3 (Group like terms and then simplify).

Conclusion: 3x - 2 Remains Unchanged

In conclusion, the algebraic expression 3x - 2 is already in its simplest form. We cannot simplify it further because 3x and -2 are unlike terms. Remember, simplification involves combining like terms. Understanding like and unlike terms is key to mastering the simplification of algebraic expressions.