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1/4(8x - 16) = 14 - x

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To determine whether the equation \( \frac{1}{4}(8x - 16) = 14 - x \) has one solution, no solutions, or infinitely many solutions, we need to simplify and solve it step by step.

  1. Simplify the Left Side: \[ \frac{1}{4}(8x - 16) = 2x - 4 \]

  2. Rewrite the Equation: \[ 2x - 4 = 14 - x \]

  3. Get all terms involving \( x \) on one side: \[ 2x + x = 14 + 4 \]

  4. Combine like terms: \[ 3x = 18 \]

  5. Solve for \( x \): \[ x = \frac{18}{3} = 6 \]

The solution to the equation is \( x = 6 \).

Since we found one specific solution, the equation has one solution.