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Chapter 1: Problem 1

Perform the indicated operation and simplify. $$(3 x+2)-(5 x+1)$$

Short Answer

Expert verified
-2x + 1

Step by step solution

01

Distribute the subtraction

Remove the parentheses and distribute the subtraction sign to both terms in the second parentheses. The expression becomes: (3x + 2) - 5x - 1.
02

Combine like terms

Combine the terms that contain the variable x and the constant terms separately. Group 3x and -5x together and 2 and -1 together. (3x - 5x) + (2 - 1).
03

Simplify the expression

Simplify the grouped terms. 3x - 5x = -2x 2 - 1 = 1 Combine these results to get the final simplified expression: -2x + 1.

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Key Concepts

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

Combining Like Terms
Combining like terms is a crucial step in simplifying algebraic expressions. Like terms are terms that have the same variables raised to the same power. For example, in the expression from our problem, we look at the terms involving the variable x (3x and -5x) and the constants (2 and -1). Make sure to group them together based on these categories. This makes it easier to combine and simplify.
Distributive Property
The distributive property helps in simplifying expressions where you have parentheses. When we distribute the subtraction sign to both terms inside the parentheses, it affects each term separately. For example, in the given problem, we start with (3x + 2) - (5x + 1). Applying the subtraction to both 5x and 1 changes the expression to (3x + 2) - 5x - 1. This removes the parentheses, making it easier to combine like terms later.
Simplifying Expressions
Simplifying expressions involves a series of steps: removing parentheses (if any), combining like terms, and performing the arithmetic operations. In our exercise, after distributing the subtraction and combining like terms, the final step is simplifying. 3x - 5x simplifies to -2x and 2 - 1 simplifies to 1. The simplified expression results in: -2x + 1. It's that simple!

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