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

Question

A. 2x - 6 = 18
B. 2x - 3 = 18
C. x - 4 = 14
D. x-3/18 = 2

Answer 1

To find an equivalent equation to $\frac{18}{x}-3=2$, we can start by solving for $x$ in the original equation.

1. First, add 3 to both sides: $$\frac{18}{x}=5$$

2. Then multiply both sides by $x$ to eliminate the fraction: $$18=5x$$

3. Now, divide both sides by 5: $$x=\frac{18}{5}$$

Now, let's analyze the provided options to see which one has the same solution:

A. $2x-6=18$ $$2x=24x=12$$

B. $2x-3=18$ $$2x=21x=10.5$$

C. $x-4=14$ $$x=18$$

D. $\frac{x-3}{18}=2$ Multiply both sides by 18: $$x-3=36x=39$$

None of these options yield the solution $x=\frac{18}{5}$, which is $3.6$.

However, let's re-evaluate option D:

Starting with $\frac{x-3}{18}=2$:

1. Multiply both sides by 18: $$x-3=36$$
2. Solve for $x$: $$x=39$$

None of the options have the same solution as the original equation. Thus, none of the provided options are equivalent to $\frac{18}{x}-3=2$ based on the calculations. The answer is that none of them have the same solution. If you want to adjust and review the options again or present alternative options, please feel free to share!