In Exercises 85–96, simplify each algebraic expression. 2(5x−1)+14x

Verified step by step guidance

1. Distribute the 2 across the terms inside the parentheses. Multiply 2 by each term in the expression (5x - 1), resulting in 2 * 5x and 2 * -1.
2. Simplify the distributed terms. This gives 10x - 2.
3. Combine the simplified expression (10x - 2) with the remaining term, 14x, from the original expression.
4. Group the like terms together. In this case, combine the x terms (10x and 14x) and leave the constant term (-2) as is.
5. Simplify the grouped terms to get the final simplified expression.

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 set of parentheses. In the given expression, applying the distributive property to 2(5x - 1) means multiplying 2 by both 5x and -1, which simplifies the expression effectively.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. In the expression, after distributing, you will have terms with 'x' and constant terms. Grouping these similar terms together allows for simplification, leading to a more concise expression.

Simplifying Algebraic Expressions

Simplifying algebraic expressions means rewriting them in a more compact form without changing their value. This process often involves using the distributive property, combining like terms, and performing any necessary arithmetic operations. The goal is to express the original expression in its simplest form, making it easier to understand and work with.