Question

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

Answer 1

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**