Problem 11 - Beginning and Intermediate Algebra

Question

Simplify each expression. 5+2(x-3 y)$

Step-by-Step Solution

Answer

5 + 2x - 6y

Step 1: Distribute the 2 inside the parentheses

Apply the distributive property to the term inside the parentheses. Multiply 2 by both terms inside the parentheses: 5 + 2(x - 3y) = 5 + 2x - 6y

Step 2: Combine like terms

In this case, there are no like terms to combine. The simplified expression is: 5 + 2x - 6y

Key Concepts

Distributive Property

The distributive property is an important rule in algebra. It's how we simplify expressions by distributing a term across terms inside parentheses. For example, in the expression 5 + 2(x - 3y), we apply the distributive property to eliminate the parentheses. This means you multiply the 2 outside by each term inside: 2 times x and 2 times -3y. So the formula is: 5 + 2x - 6y. This process helps in organizing and simplifying algebraic expressions, making them easier to handle.

Combining Like Terms

Combining like terms is another crucial step in simplifying algebraic expressions. Like terms are terms that have the same variables raised to the same power. In our example, 5 + 2x - 6y, we look for like terms to combine. However, since 5, 2x, and -6y are all different types of terms (constant, x-term, and y-term), we can't combine any of them. Combining like terms helps condense expressions into their simplest form, which simplifies calculations.

Algebraic Expressions

An algebraic expression is a combination of numbers, variables, and operations. Expressions can include constants (like 5), variables (like x and y), and coefficients (like 2 in 2x). Simplifying algebraic expressions involves applying the distributive property, combining like terms, and reducing the expression into the simplest form. The original expression, 5 + 2(x - 3y), breaks down to the simplified form, 5 + 2x - 6y, through these steps. Mastering this process is key to success in algebra and higher math.