Simplify the algebraic expression. 5(2x - 3) + 7x

Verified step by step guidance

1. Distribute the 5 into the terms inside the parentheses: 5 * 2x and 5 * (-3).
2. This gives you: 10x - 15.
3. Now, add the 7x to the expression: 10x - 15 + 7x.
4. Combine like terms: 10x and 7x.
5. Simplify the expression by adding the coefficients of x: (10 + 7)x - 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 set of parentheses. In the expression 5(2x - 3), we apply this property to distribute 5 to both 2x and -3, resulting in 10x - 15.

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, we will have terms with 'x' and constant terms. For example, in 10x - 15 + 7x, we can combine 10x and 7x to simplify the expression further.

Simplifying Expressions

Simplifying expressions means rewriting them in a more concise form without changing their value. This process often involves using the Distributive Property and combining like terms. The goal is to express the algebraic expression in its simplest form, making it easier to understand and work with.