Verified Answer :

  • Apply the distributive property by multiplying 3 by each term inside the parentheses: \(3 \cdot 5x = 15x\) and \(3 \cdot 4 = 12\).
  • Combine these results to form the simplified expression: \(15x - 12\).
  • Select the option that matches the result: \(\boxed{15x - 12}\).

Explanation

  1. Understanding the Problem and Applying the Distributive Property

The given expression is \(3(5x - 4)\). To simplify this, we need to distribute the scalar \(3\) across each term inside the parentheses. This is an application of the distributive property of multiplication over subtraction, which states that \(a(b - c) = ab - ac\).

  1. Performing the Calculation

Applying the property:
\[3(5x - 4) = 3 \cdot (5x) - 3 \cdot (4)\]
Now perform the multiplications:
\[3 \cdot 5x = 15x\]
\[3 \cdot 4 = 12\]
Subtracting these results, we get the simplified expression:
\[15x - 12\]

  1. Conclusion and Final Answer

Comparing our result with the given options, we identify that the simplified expression is \(15x - 12\). Therefore, the correct option is the second one. The final answer is \(\boxed{15x - 12}\).

Examples

Imagine you are purchasing 3 identical packages of notebooks, where each package contains 5 notebooks and has a \$4 rebate. The total cost, represented by the variable @@MATH_TOKEN_13@@ for the price per notebook, is @@MATH_TOKEN_14@@. Simplifying this expression helps you quickly calculate the net price: @@MATH_TOKEN_15@@, meaning you pay for 15 notebooks and receive a total of \$12 back in rebates. This demonstrates how algebraic simplification makes managing costs or resources more efficient in everyday shopping or planning.

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