To solve the equation step by step, let's follow the provided steps and fill in the missing components:
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Start with the original equation: \[ -17(4q - 2) + 3q = -18q - 13 \]
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Apply the distributive property: \[ -17 \cdot 4q + (-17) \cdot (-2) + 3q = -18q - 13 \] This simplifies to: \[ -68q + 34 + 3q = -18q - 13 \]
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Combine like terms on the left: \[ (-68q + 3q) + 34 = -18q - 13 \] This simplifies to: \[ -65q + 34 = -18q - 13 \]
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Now, add \( 18q \) to both sides: \[ -65q + 18q + 34 = -13 \] This simplifies to: \[ -47q + 34 = -13 \]
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Now, subtract \( 34 \) from both sides: \[ -47q = -13 - 34 \] This simplifies to: \[ -47q = -47 \]
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Finally, divide both sides by \( -47 \): \[ q = 1 \]
Now, filling in and indicating what actions we took based on the provided structure:
Filled Missing Terms and Descriptions:
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After applying the distributive property: \[ -68q + 34 + 3q = -18q - 13 \]
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Combining like terms: \[ -65q + 34 = -18q - 13 \]
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Add \( 18q \) to both sides: \[ -47q + 34 = -13 \]
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Subtract \( 34 \) from both sides: \[ -47q = -47 \]
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Divide both sides by (-47): \[ q = 1 \]
So the compiled process shows how we solve for \( q \), filling in the necessary terms and describing the steps taken correctly.