How many solutions does this equation have? Solve on paper and enter your answer on Zearn.

6x = 1/6 (36x+6)

A.No solutions

B.One solution

C.Infinitely many solutions

1 answer

To solve the equation \( 6x = \frac{1}{6} (36x + 6) \), let's start by simplifying it step by step.

  1. Multiply both sides of the equation by 6 to eliminate the fraction: \[ 6 \cdot (6x) = 6 \cdot \left(\frac{1}{6} (36x + 6)\right) \] This simplifies to: \[ 36x = 36x + 6 \]

  2. Next, we can rearrange the equation by subtracting \( 36x \) from both sides: \[ 36x - 36x = 36x + 6 - 36x \] Which simplifies to: \[ 0 = 6 \]

  3. The equation \( 0 = 6 \) is a contradiction, which indicates that there are no values for \( x \) that can satisfy the original equation.

Thus, the equation has no solutions.

The answer is: A. No solutions