Lesson 7 Homework Practice Subtract Linear Expressions

How to Subtract Linear Expressions: A Step-by-Step Guide

A linear expression is an algebraic expression that contains only constants and variables with no exponents or radicals. For example, 3x - 5 and -2y + 7 are linear expressions, but x^2 + 4 and \\sqrt{y} - 3 are not.

To subtract linear expressions, we need to apply the distributive property and combine like terms. The distributive property states that a(b - c) = ab - ac, which means we can multiply a term outside a parenthesis by each term inside the parenthesis and then subtract the results. Like terms are terms that have the same variable and the same exponent, such as 2x and -5x, or 7 and -3. To combine like terms, we add or subtract their coefficients (the numbers in front of the variables).

Here are the steps to subtract linear expressions:

Rewrite the subtraction as an addition of the opposite. For example, 3x - 5 - (2x + 7) can be rewritten as 3x - 5 + (-2x - 7).

Distribute any negative signs to remove the parentheses. For example, 3x - 5 + (-2x - 7) can be simplified as 3x - 5 - 2x - 7.

Combine like terms by adding or subtracting their coefficients. For example, 3x - 5 - 2x - 7 can be simplified as x - 12, since 3x - 2x = x and -5 - 7 = -12.

Write the final answer in descending order of the variables. For example, x - 12 is already in descending order, since x comes before any constant.

Let's try an example: Subtract -4y + 9 - (3y - 6).

Rewrite the subtraction as an addition of the opposite: -4y + 9 + (-3y + 6).

Distribute any negative signs to remove the parentheses: -4y + 9 - 3y + 6.

Combine like terms by adding or subtracting their coefficients: -7y + 15, since -4y - 3y = -7y and 9 + 6 = 15.

Write the final answer in descending order of the variables: -7y + 15.

The answer is -7y + 15.

If we want to subtract more than two linear expressions, we can follow the same steps as before, but we need to be careful with the signs. For example, let's subtract 2x - 3, -x + 5, and 4x - 7.

Rewrite the subtraction as an addition of the opposite: 2x - 3 + (-(-x + 5)) + (-(4x - 7)).

Distribute any negative signs to remove the parentheses: 2x - 3 + x - 5 - 4x + 7.

Combine like terms by adding or subtracting their coefficients: -x - 1, since 2x + x - 4x = -x and -3 - 5 + 7 = -1.

Write the final answer in descending order of the variables: -x - 1.

The answer is -x - 1. 061ffe29dd