Question
What equation has the same solution as this equation?: 18/x-3 = 2
A. 2x - 6 = 18
B. 2x - 3 = 18
C. x - 4 = 14
D. x-3/18 = 2
A. 2x - 6 = 18
B. 2x - 3 = 18
C. x - 4 = 14
D. x-3/18 = 2
Answers
GPT-4o mini
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. \( 2x - 6 = 18 \)
\[
2x = 24 \\
x = 12
\]
B. \( 2x - 3 = 18 \)
\[
2x = 21 \\
x = 10.5
\]
C. \( x - 4 = 14 \)
\[
x = 18
\]
D. \( \frac{x-3}{18} = 2 \)
Multiply both sides by 18:
\[
x - 3 = 36 \\
x = 39
\]
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!
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. \( 2x - 6 = 18 \)
\[
2x = 24 \\
x = 12
\]
B. \( 2x - 3 = 18 \)
\[
2x = 21 \\
x = 10.5
\]
C. \( x - 4 = 14 \)
\[
x = 18
\]
D. \( \frac{x-3}{18} = 2 \)
Multiply both sides by 18:
\[
x - 3 = 36 \\
x = 39
\]
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!