In Exercises 117–130, simplify each algebraic expression. 8(3x-5)-6x

Verified step by step guidance

1. Distribute the 8 across the terms inside the parentheses: 8 \times 3x and 8 \times (-5).
2. This results in: 24x - 40.
3. Now, combine like terms: 24x and -6x.
4. Subtract 6x from 24x to simplify the expression.
5. The simplified expression is in terms of x.

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. In the expression 8(3x - 5), we apply this property to distribute 8 to both 3x and -5, resulting in 24x - 40.

Combining Like Terms

Combining like terms involves simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. In the expression 24x - 40 - 6x, we can combine the x terms (24x and -6x) to simplify the expression further to 18x - 40.

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.