Adding and Subtracting Linear Expressions

Front

What is a linear expression?

Back

A linear expression is an algebraic expression in which each term is either a constant or the product of a constant and a single variable raised to the first power.

Front

What does it mean to add linear expressions?

Back

Adding linear expressions involves combining like terms to simplify the expression.

Front

What does it mean to subtract linear expressions?

Back

Subtracting linear expressions involves changing the signs of the terms in the expression being subtracted and then combining like terms.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms.

Front

How do you combine like terms in the expression (5x - 6) - (x + 2)?

Back

First, distribute the negative sign: 5x - 6 - x - 2. Then combine like terms: (5x - x) + (-6 - 2) = 4x - 8.

Front

What is the result of (7a + 4) - (9a + 2)?

Back

The result is -2a + 2.

Front

How do you find the sum of (3x + 5) + (2x + 1)?

Back

Combine like terms: (3x + 2x) + (5 + 1) = 5x + 6.

Front

What is the sum of (7k - 9) + (-4k + 3)?

Back

The sum is 3k - 6.

Front

How do you simplify the expression (−x + 8) + (−5x − 1)?

Back

Combine like terms: (-x - 5x) + (8 - 1) = -6x + 7.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a parenthesis.