Let's complete and simplify the process step by step:
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Starting from the original equation: \[ 17(4x + 1) + 14x = -17x + 17 \]
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Apply the distributive property to the left side: \[ 68x + 17 + 14x = -17x + 17 \]
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Combine like terms on the left side: \[ 82x + 17 = -17x + 17 \]
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Subtract 17 from both sides: \[ 82x = -17x \]
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Add \( 17x \) to both sides: \[ 82x + 17x = 0 \] \[ 99x = 0 \]
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Subtract 17 from both sides: (Note: This step was unnecessary here but can be done if equating to a constant.) \[ 99x = 0 \]
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Divide both sides by 99: \[ x = 0 \]
So, the complete process including the filled in blanks and selections would look like this:
- \( 99x = 0 \)
- \( x = 0 \)
The final solution is \( x = 0 \).
Now we determine the missing descriptions:
- Apply the distributive property
- Combine like terms
- Add 17x to both sides
- Divide both sides by 99
These actions reflect the operations conducted to solve the original equation step by step.