Question

which of the following values will make the equation true for no values of x for the equation 3x + 6 = 3(x + □)? select three answers. a 8 b 2 c 6 d 4

Explanation:

Step1: Simplify the right side

First, we expand the right - hand side of the equation \(3(x + \square)\) using the distributive property \(a(b + c)=ab+ac\). So, \(3(x+\square)=3x + 3\times\square\). The original equation is \(3x + 6=3x+3\times\square\).

Step2: Analyze the equation type

Subtract \(3x\) from both sides of the equation. We get \(6 = 3\times\square\). If \(3\times\square
eq6\), then the equation \(3x + 6=3(x + \square)\) will have no solution for \(x\).

Step3: Solve for \(\square\) when there is no solution

We solve the equation \(3\times\square=6\) for \(\square\). Dividing both sides by 3, we find that \(\square = 2\). So, when \(\square
eq2\), the equation \(3x + 6 = 3(x+\square)\) has no solution for \(x\).

Now we check each option:

• Option A: If \(\square = 8\), then \(3\times8 = 24

eq6\), so the equation has no solution.

• Option B: If \(\square=2\), then \(3\times2 = 6\), and the equation \(3x + 6=3x + 6\) is true for all values of \(x\) (not no values of \(x\)).
• Option C: If \(\square = 6\), then \(3\times6=18

eq6\), so the equation has no solution.

• Option D: If \(\square = 4\), then \(3\times4 = 12

eq6\), so the equation has no solution.

Answer:

A. 8, C. 6, D. 4