Which situations can represent the expression 6−x

Question

? Check the three that apply.(3 points)
Responses

Six servings of dinner were decreased by a number.
Six servings of dinner were decreased by a number.

Gabrielle decreased her 6-minute mile by an unknown amount of time.
Gabrielle decreased her 6-minute mile by an unknown amount of time.

Benjamin lost six of his stickers.
Benjamin lost six of his stickers.

Naomi gives some of her six pencils away.
Naomi gives some of her six pencils away.

Westville has 6 fewer schools than Eastville.
Westville has 6 fewer schools than Eastville.

Sydney increased her collection of coins by six.
Sydney increased her collection of coins by six.

Answer 1

The expression \(6 - x\) represents a situation where something starts at 6 and then decreases by an unknown amount \(x\). Here are the options that apply:

1. Six servings of dinner were decreased by a number.
   This directly represents the expression \(6 - x\) where \(x\) is the number of servings decreased.

2. Gabrielle decreased her 6-minute mile by an unknown amount of time.
   This also fits the expression \(6 - x\), where \(x\) is the unknown time reduced from her 6 minutes.

3. Naomi gives some of her six pencils away.
   This situation fits as well. The six pencils are decreased by an unknown number \(x\) (the pencils she gives away), which can also be represented as \(6 - x\).

The other options do not represent \(6 - x\):

• Benjamin lost six of his stickers does not fit because it signifies a fixed loss, not a variable decrease from 6.

• Westville has 6 fewer schools than Eastville implies a difference rather than a reduction starting from 6.

• Sydney increased her collection of coins by six implies an increase, which does not relate to a decrease from 6.

So the three situations that apply are:

1. Six servings of dinner were decreased by a number.
2. Gabrielle decreased her 6-minute mile by an unknown amount of time.
3. Naomi gives some of her six pencils away.