Which of the following equations has the same solution as the equation above? 18/x-3 = 2

Answer 1

To solve for $x$ in the equation $\frac{18}{x}-3=2$, we will first isolate $\frac{18}{x}$.

1. Add 3 to both sides of the equation: $$\frac{18}{x}=2+3$$ $$\frac{18}{x}=5$$

2. Now, multiply both sides by $x$ (assuming $x\ne 0$): $$18=5x$$

3. Divide both sides by 5: $$x=\frac{18}{5}$$

Now that we have the solution $x=\frac{18}{5}$, we can write an equivalent equation.

To derive equations that are equivalent:

1. We can start from the original equation $\frac{18}{x}-3=2$ and transform it to a similar format.

2. Multiply through by $x$ (as indicated earlier): $$18-3x=2x$$

3. Rearranging gives us: $$18=2x+3x$$ $$18=5x$$

This final expression $5x=18$ is equivalent to the original equation.

So an equation with the same solution as $\frac{18}{x}-3=2$ would be: $$5x=18$$

If there are any other options specified, please provide them, and I can confirm which one(s) also has the same solution.