Verified Answer :

  • Apply the distributive property to distribute \(\frac{1}{3}\) over the terms in the parentheses.
  • Multiply \(\frac{1}{3}\) by \(-18x\) to get \(-6x\).
  • Multiply \(\frac{1}{3}\) by \(36\) to get \(12\).
  • Combine the terms to reach the final simplified expression \(\boxed{-6x + 12}\).

Explanation

  1. Analysis of the Expression

We are tasked with simplifying the expression \(\frac{1}{3}(-18x + 36)\). This expression consists of a scalar factor \(\frac{1}{3}\) multiplying a binomial \((-18x + 36)\). Our goal is to simplify this using the distributive property, which states that \(a(b + c) = ab + ac\).

  1. Applying the Distributive Property

To simplify \(\frac{1}{3}(-18x + 36)\), we distribute the \(\frac{1}{3}\) to each term inside the parentheses:
\[\frac{1}{3}(-18x + 36) = \frac{1}{3} \cdot (-18x) + \frac{1}{3} \cdot 36\]
Now, we perform the multiplication for each term:

  1. For the first term: \(\frac{1}{3} \cdot (-18x) = -6x\)
  2. For the second term: \(\frac{1}{3} \cdot 36 = 12\)
  1. Final Simplification

By combining the results of the multiplications from the previous step, we obtain:
\[-6x + 12\]
Thus, the expression \(\frac{1}{3}(-18x + 36)\) simplifies to \(-6x + 12\).

Examples

In real-world applications, such as calculating the net change in a budget or tracking variable costs, we often encounter grouped terms that need to be scaled. For example, if you are calculating the reduction of three equal installments of a total cost represented by \((-18x + 36)\), you would divide the entire expression by 3 to find the value of each installment. Simplifying such expressions helps in quickly determining the net impact on your final balance.

Related Questions