Problem 39 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$\frac{1}{2}(5 x-12)$$

Step-by-Step Solution

Answer

The expression \(\frac{1}{2}(5x - 12)\) can be simplified to \(2.5x - 6\) without parentheses.

Step 1: Identify the Factors

Here the factors being distribute are \(\frac{1}{2}\) and \(5x - 12\). The number \(\frac{1}{2}\) is to be distributed inside the parentheses.

Step 2: Apply the Distributive Property

Implementing the distributive property, multiply \(\frac{1}{2}\) by each of the terms inside the parentheses, resulting in \(\frac{1}{2}\)*\(5x\) and \(\frac{1}{2}\)*\(-12\).

Step 3: Simplify the Expression

Multiplying the factors simplifies the expression to \(2.5x\) - \(6\).