Question

Solve.

18/x−3 = 2

Which of the following equations has the same solution as the equation above?

(1 point)
Responses

x−4=14

2x−3=18

2x−6=18

x−3/18 = 2

Answer 1

Let's solve the original equation first:

\[
\frac{18}{x} - 3 = 2
\]

To isolate the term with \(x\), add \(3\) to both sides:

\[
\frac{18}{x} = 2 + 3
\]
\[
\frac{18}{x} = 5
\]

Next, multiply both sides by \(x\) to eliminate the fraction:

\[
18 = 5x
\]

Now, divide both sides by \(5\):

\[
x = \frac{18}{5}
\]

Now, we need to check which of the provided equations has the same solution \(x = \frac{18}{5}\).

1. **For \(x - 4 = 14\)**:
\[
x = 14 + 4 = 18 \quad \text{(Not the same)}
\]

2. **For \(2x - 3 = 18\)**:
\[
2x = 18 + 3 = 21
\]
\[
x = \frac{21}{2} \quad \text{(Not the same)}
\]

3. **For \(2x - 6 = 18\)**:
\[
2x = 18 + 6 = 24
\]
\[
x = \frac{24}{2} = 12 \quad \text{(Not the same)}
\]

4. **For \(\frac{x - 3}{18} = 2\)**:
Multiply both sides by \(18\):
\[
x - 3 = 36
\]
\[
x = 36 + 3 = 39 \quad \text{(Not the same)}
\]

None of the equations provided lead to the same solution \(x = \frac{18}{5}\). Please double-check the options provided.