To determine how many solutions the equation \(-3 - 15f + 16 = -17f - 13\) has, we will first simplify and solve the equation step by step.
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Combine like terms on the left side: \[ -3 + 16 = 13 \quad \Rightarrow \quad 13 - 15f = -17f - 13 \] So the equation simplifies to: \[ 13 - 15f = -17f - 13 \]
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Next, we can add \(17f\) to both sides: \[ 13 - 15f + 17f = -13 \] This simplifies to: \[ 13 + 2f = -13 \]
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Now, we subtract \(13\) from both sides: \[ 2f = -13 - 13 \quad \Rightarrow \quad 2f = -26 \]
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Divide both sides by \(2\): \[ f = \frac{-26}{2} \quad \Rightarrow \quad f = -13 \]
The solution to the equation is \(f = -13\). Since we found one unique solution, we can conclude that:
The equation has exactly one solution.
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