Simplify each expression. See Example 8.3(k + 2) - 5k + 6 + 3

Verified step by step guidance

1. Distribute the 3 into the expression (k + 2) to get 3k + 6.
2. Rewrite the expression as 3k + 6 - 5k + 6 + 3.
3. Combine like terms: 3k and -5k to get -2k.
4. Combine the constant terms: 6, 6, and 3 to get 15.
5. Rewrite the simplified expression as -2k + 15.

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term within a parenthesis, facilitating the simplification of expressions. In the given expression, applying this property to 3(k + 2) will help in breaking it down into simpler components.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This process simplifies expressions by consolidating similar components, making calculations easier. In the expression, terms like -5k and 3k can be combined to streamline the overall expression.

Order of Operations

The Order of Operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules is crucial when simplifying expressions to avoid errors.