7.3 Adding 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 into a single linear expression.

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 (3x + 5) + (2x + 1)?

Back

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

Front

What is the sum of the expressions 2(x + 3) + (3x - 2)?

Back

First, distribute: 2x + 6 + 3x - 2 = 5x + 4.

Front

How do you simplify the expression (5 - t) + (3t + 2)?

Back

Combine like terms: (5 + 2) + (-t + 3t) = 7 + 2t = 2t + 7.

Front

What is the result of adding (-m + 3) + (7m - 1)?

Back

Combine like terms: (-m + 7m) + (3 - 1) = 6m + 2.

Front

What is the sum of the expressions (−x + 8) + (−5x − 1)?

Back

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

Front

What is the distributive property in relation to linear expressions?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a term across a sum.

Front

How do you apply the distributive property to the expression 2(x + 3)?

Back

Distribute 2: 2 * x + 2 * 3 = 2x + 6.