Problem 36 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$4(x-5)$$

Step-by-Step Solution

Answer

The expression \(4(x-5)\) rewritten using the distributive property is \(4x - 20\)

Step 1: Identify the Outside Number and Parentheses

In the expression \(4(x-5)\), the number 4 is on the outside of the parentheses and will be distributed to each term inside the parentheses, which are x and -5. The sign associated with the number is part of that number.

Step 2: Multiply the Outer Number with Each Term Inside the Parentheses

Multiply 4 by \(x\) and then by -5. This results in \(4x\) and \(-20\), respectively.

Step 3: Write the Final Answer

The new expression, after applying the distributive property, is \(4x - 20\)