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Which situations can represent the expression 8 - x? Check the three that apply.

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(3 points)
• Sydney increased her collection of stamps by eight.
Gabrielle decreased her eight-minute commute to school by some number of minutes.
• Naomi had eight pencils and gave some away to her classmates.
• Benjamin lost eight of his socks.
• Jones County has eight fewer elective courses than Smith County.
• Eight serving of lunch decreased by some number.

1 answer

To identify the situations that represent the expression \(8 - x\), we can look for scenarios where we start with eight of something and then remove or decrease that amount by some quantity \(x\). Here are the explanations for each option:

  1. Sydney increased her collection of stamps by eight.

    • This does not represent \(8 - x\) because she is gaining stamps, not losing them.

  2. Gabrielle decreased her eight-minute commute to school by some number of minutes.

    • This scenario represents \(8 - x\), where \(x\) is the number of minutes decreased from her eight-minute commute.

  3. Naomi had eight pencils and gave some away to her classmates.

    • This situation also represents \(8 - x\), where \(x\) is the number of pencils she gave away.

  4. Benjamin lost eight of his socks.

    • This does not represent \(8 - x\) because he lost a fixed amount (eight socks), not a variable amount based on some quantity \(x\) taken from eight.

  5. Jones County has eight fewer elective courses than Smith County.

    • This can also be interpreted in terms of subtraction, representing \(8 - x\) where \(x\) signifies the number of courses fewer than Smith County.

  6. Eight servings of lunch decreased by some number.

    • This represents \(8 - x\) as well, where \(x\) signifies the number of servings that were decreased from the original eight.

Based on the above reasoning, the correct situations that represent the expression \(8 - x\) are:

  • Gabrielle decreased her eight-minute commute to school by some number of minutes.
  • Naomi had eight pencils and gave some away to her classmates.
  • Jones County has eight fewer elective courses than Smith County.
  • Eight servings of lunch decreased by some number.

So the three applicable situations are:

  1. Gabrielle decreased her eight-minute commute to school by some number of minutes.
  2. Naomi had eight pencils and gave some away to her classmates.
  3. Eight servings of lunch decreased by some number.

Choose those three options and check your answer!