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

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

1 answer

To solve for \( x \) in the given equation \( \frac{18}{x} - 3 = 2 \), we can start by isolating the term involving \( x \).

  1. Add 3 to both sides:

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

  2. Multiply both sides by \( x \):

    \[ 18 = 5x \]

  3. Divide both sides by 5:

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

Now we will check each of the given options to see if any have the same solution \( x = \frac{18}{5} \).

Option A: \( 2x - 6 = 18 \)

  1. Add 6 to both sides:

    \[ 2x = 24 \]

  2. Divide both sides by 2:

    \[ x = 12 \] (No match)

Option B: \( 2x - 3 = 18 \)

  1. Add 3 to both sides:

    \[ 2x = 21 \]

  2. Divide both sides by 2:

    \[ x = \frac{21}{2} \] (No match)

Option C: \( x - 4 = 14 \)

  1. Add 4 to both sides:

    \[ x = 18 \] (No match)

Option D: \( \frac{x-3}{18} = 2 \)

  1. Multiply both sides by 18:

    \[ x - 3 = 36 \]

  2. Add 3 to both sides:

    \[ x = 39 \] (No match)

Since none of the options provided yields \( x = \frac{18}{5} \), it appears that none of the options provided share the same solution. If there's any further clarification needed, please let me know!