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What value will complete the set of equations 15/

3x−9−4=12
and x≠
_____?(1 point)
The value that completes the set of equations is x≠

1 answer

To solve the equation \( \frac{15}{3x - 9} - 4 = 12 \), we first isolate the fraction:

  1. Add 4 to both sides: \[ \frac{15}{3x - 9} = 12 + 4 \] \[ \frac{15}{3x - 9} = 16 \]

  2. Now, cross-multiply to eliminate the fraction: \[ 15 = 16(3x - 9) \]

  3. Distribute the 16: \[ 15 = 48x - 144 \]

  4. Rearranging gives: \[ 48x = 15 + 144 \] \[ 48x = 159 \]

  5. Now, solve for \( x \): \[ x = \frac{159}{48} \]

Next, we must determine any restrictions on \( x \). The original equation contains a fraction, which means the denominator cannot be zero. Set the denominator equal to zero and solve for \( x \): \[ 3x - 9 = 0 \] \[ 3x = 9 \] \[ x = 3 \]

Thus, the value that completes the set of equations is \( x \neq 3 \).

So the final answer is: \[ \text{The value that completes the set of equations is } x \neq 3. \]