Question

1. complete the tables to determine if the expressions are equivalent. if the expressions are equivalent, name the property or properties that make them equivalent.

x	value of expression

x	value of expression

Explanation:

Step1: Analyze the first expression

We have the expression \(3(x - 5)\). Using the distributive property \(a(b - c)=ab - ac\), where \(a = 3\), \(b=x\) and \(c = 5\), we get \(3\times x-3\times5=3x - 15\).

Step2: Compare with the second expression

The second expression is \(3x-15\). Since after expanding \(3(x - 5)\) we get \(3x - 15\), the two expressions are equivalent by the distributive property.

Answer:

The expressions \(3(x - 5)\) and \(3x-15\) are equivalent by the distributive property.