Question

multiple choice
complete the equation with the number or variable term that will make the equation true for all values of x.
3x + 6 = 3(x + □)
a 2
b 6
c 3
d 5

Explanation:

Step1: Apply Distributive Property

The distributive property states that \( a(b + c)=ab + ac \). For the right - hand side of the equation \( 3(x+\square) \), using the distributive property, we get \( 3\times x+3\times\square=3x + 3\square \).

Step2: Set Up the Equation

We know that the left - hand side of the original equation is \( 3x + 6 \), and the right - hand side after applying the distributive property is \( 3x+3\square \). Since the equation \( 3x + 6=3(x+\square) \) is true for all values of \( x \), the constant terms must be equal. So we set up the equation \( 3\square=6 \).

Step3: Solve for \(\square\)

To solve for \(\square\) in the equation \( 3\square = 6 \), we divide both sides of the equation by 3. \(\square=\frac{6}{3}=2\).

Answer:

A. 2