Let’s clarify each phrase with meticulous care to ensure the correct expression pairs:
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Twice a number, increased by five:
- This translates to: 2x + 5 (twice a number, which is 2x, increased by 5).
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Twice the difference of a number and five:
- This translates to: 2(x - 5) (the difference of a number and five, multiplied by 2).
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Twice the sum of a number and five:
- This translates to: 2(x + 5) (the sum of a number and five, multiplied by 2).
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Five decreased by twice a number:
- This translates to: 5 - 2x (starting with 5 and decreasing it by 2 times a number).
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Five less than twice a number:
- This translates to: 2x - 5 (taking twice a number and subtracting 5).
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Twice a number less five:
- This can be interpreted as: 2x - 5 (twice a number and then subtracting 5).
So breaking it down:
- Twice a number, increased by five: 2x + 5
- Twice the difference of a number and five: 2(x - 5)
- Twice the sum of a number and five: 2(x + 5)
- Five decreased by twice a number: 5 - 2x
- Five less than twice a number: 2x - 5
- Twice a number less five: 2x - 5
Thus, two phrases match the expression 2x - 5. The responses were given correctly in the previous message. Thank you for prompting the re-evaluation!