Problem 40 - Introductory Algebra for College Students

Question

Use a form of the distributive property to rewrite each algebraic expression without parentheses. $$\frac{1}{3}(7 x-21)$$

Step-by-Step Solution

Answer

The simplified form of the expression \(\frac{1}{3}(7x-21)\) is \(\frac{7}{3}x - 7\).

Step 1: Use Distributive Property

To simplify this expression, use the distributive property by multiplying \(\frac{1}{3}\) with each term inside the parentheses. This could be written as \(\frac{1}{3} * 7x - \frac{1}{3} * 21\).

Step 2: Calculate the Multiplication

Now perform the multiplication: \(\frac{7}{3}x - \frac{21}{3}\).

Step 3: Simplify the Expressions

Finally, simplify the right term \(\frac{21}{3}\) to its simplest form which is 7. Now you have the expression : \(\frac{7}{3}x - 7\).