(4x-5y)+(6x+3)-(7x-2y)

2 min read Jun 16, 2024

Simplifying Algebraic Expressions: (4x - 5y) + (6x + 3) - (7x - 2y)

This article will guide you through the process of simplifying the algebraic expression: (4x - 5y) + (6x + 3) - (7x - 2y).

Before we dive in, let's remember some key concepts:

Terms: Individual parts of an expression separated by addition or subtraction signs. For example, in (4x - 5y), '4x' and '5y' are individual terms.
Like Terms: Terms that have the same variables raised to the same powers. For instance, '3x' and '7x' are like terms because they both have 'x' raised to the power of 1.
Combining Like Terms: This is the core of simplifying algebraic expressions. We combine the coefficients (the numerical part) of like terms while keeping the variable and its power the same.

Remove Parentheses: We start by removing the parentheses. Remember that a minus sign before parentheses changes the sign of each term inside.

(4x - 5y) + (6x + 3) - (7x - 2y) becomes 4x - 5y + 6x + 3 - 7x + 2y
Identify Like Terms: Now, let's group the like terms together:
- x terms: 4x + 6x - 7x
- y terms: -5y + 2y
- Constant term: 3
Combine Like Terms: We combine the coefficients of each group:
- x terms: (4 + 6 - 7)x = 3x
- y terms: (-5 + 2)y = -3y
Write the Simplified Expression: Now we can write the simplified expression: 3x - 3y + 3

The simplified form of the expression (4x - 5y) + (6x + 3) - (7x - 2y) is 3x - 3y + 3.