To solve the equation \( 24(34 + x) = 1,200 \), we can break down each step and explain the reasoning behind each operation.
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Start with the original equation: \[ 24(34 + x) = 1,200 \]
- Reason: This is the initial setup of the equation that we want to solve.
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Divide both sides of the equation by 24: \[ 34 + x = \frac{1,200}{24} \]
- Reason: To isolate the term \( (34 + x) \) on one side of the equation, we can eliminate the coefficient of 24 by performing the same operation (division) on both sides. This is permissible due to the properties of equality, which state that if two values are equal, dividing (or multiplying) both by the same non-zero number will maintain the equality.
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Calculate the division: \[ 34 + x = 50 \]
- Reason: Performing the calculation \( \frac{1,200}{24} \) yields 50. This step simplifies the equation to make it easier to solve for \( x \).
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Subtract 34 from both sides: \[ x = 50 - 34 \]
- Reason: To isolate \( x \), we subtract 34 from both sides of the equation. This step uses the property of equality that if two expressions are equal, we can subtract the same number from both sides without changing the equality.
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Calculate the subtraction: \[ x = 16 \]
- Reason: After performing the subtraction \( 50 - 34 \), we find that \( x \) equals 16. This provides the solution to the original equation.
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Final answer: \[ x = 16 \]
- Reason: This is the final value that satisfies the original equation.
Overall, each step systematically removes complexity from the equation while maintaining equality, leading to the solution.