Question

What equation has the same solution as this equation?: 18/x-3 = 2

Answer 1

To find an equation that has the same solutions as the given equation \( \frac{18}{x} - 3 = 2 \), we first need to solve the original equation.

1. Start with the original equation:
\[
\frac{18}{x} - 3 = 2
\]

2. Add 3 to both sides:
\[
\frac{18}{x} = 5
\]

3. Multiply both sides by \( x \) (assuming \( x \neq 0 \)):
\[
18 = 5x
\]

4. Divide both sides by 5:
\[
x = \frac{18}{5}
\]

Now, to create a new equation that has the same solution \( x = \frac{18}{5} \), we can rearrange our original equation or manipulate it differently.

One straightforward approach is to multiply both sides of the equation \( \frac{18}{x} - 3 = 2 \) by \( x \):

1. Starting from:
\[
\frac{18}{x} - 3 = 2
\]

2. Multiply through by \( x \) (again, assuming \( x \neq 0 \)):
\[
18 - 3x = 2x
\]

3. Rearranging gives:
\[
18 = 2x + 3x
\]
\[
18 = 5x
\]

Or we could formulate a different type of equation by isolating \( x \):

From \( 5x = 18 \), we can say:
\[
5x - 18 = 0
\]

Thus, the equation \( 5x - 18 = 0 \) has the same solution as the original equation \( \frac{18}{x} - 3 = 2 \).