Solve the equation 18x = 6(x - 1)

What is 18x divided by 6?

____ x = x - 1

1 answer

To solve the equation \( 18x = 6(x - 1) \), we'll first distribute the right side:

\[ 18x = 6x - 6. \]

Next, we'll isolate \( x \) by subtracting \( 6x \) from both sides:

\[ 18x - 6x = -6, \]

which simplifies to:

\[ 12x = -6. \]

Now, divide both sides by \( 12 \):

\[ x = -\frac{6}{12} = -\frac{1}{2}. \]

So, the solution to the equation is:

\[ x = -\frac{1}{2}. \]

Now, to find \( \frac{18x}{6} \):

\[ \frac{18x}{6} = 3x. \]

Substituting \( x = -\frac{1}{2} \) into \( 3x \):

\[ 3x = 3 \left(-\frac{1}{2}\right) = -\frac{3}{2}. \]

Thus, the answer is:

\[ -\frac{3}{2}. \]

To recap:

  1. The solution to the equation is \( x = -\frac{1}{2} \).
  2. \( \frac{18x}{6} = -\frac{3}{2} \).