Let's solve the equation step-by-step starting from the original expression:
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Start with the equation: \[ 22f - 10 = -10f - 8 + 10f + 10f \]
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Simplify the right side: \[ -10f + 10f + 10f = 10f \] So the equation becomes: \[ 22f - 10 = 10f - 8 \]
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Now, add \(10\) to both sides to eliminate the constant on the left: \[ 22f - 10 + 10 = 10f - 8 + 10 \] Which simplifies to: \[ 22f = 10f + 2 \]
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Next, subtract \(10f\) from both sides: \[ 22f - 10f = 2 \] That simplifies to: \[ 12f = 2 \]
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Finally, divide both sides by \(12\) to solve for \(f\): \[ f = \frac{2}{12} = \frac{1}{6} \]
Thus, the solution is: \[ \boxed{\frac{1}{6}} \]