Which expression is equivalent to 17x−10+3(2x+1)17x−10+3(2x+1) ?(1 point) Responses 11x−711x−711 x minus 7 23x−923x−923 x minus 9 23x−723x−723 x minus 7 11x−9

Question

Simone applied the distributive property using the greatest common factor to determine the expression that is equivalent to 24+5624+56 . Her work is shown below. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 24+56=8(4+7)24+56=8(4+7) What statement best describes Simone's error? (1 point) Responses Simone did not use the greatest common factor in the equation. Simone did not use the greatest common factor in the equation. Simone did not use the correct factors for 24 in the equation. Simone did not use the correct factors for 24 in the equation. Simone did not use the correct factors for 56 in the equation. Simone did not use the correct factors for 56 in the equation. Simone did not use the correct operations in the equation.
Which expression can be used to model the statement, "On Wednesday, Nathaniel earned $10 less than he earned on Tuesday"?(1 point) Responses n−10n−10n minus 10 n+10n+10n plus 10 10<n10<n10<n10<n 10−n
Which situations can represent the expression 6−x ? 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. 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. Benjamin lost six of his stickers. Benjamin lost six of his stickers. Gabrielle decreased her 6-minute mile by an unknown amount of time.

Answer 1

Let's solve each of your questions one by one.

1. Equivalent Expression for \(17x−10+3(2x+1)\)

First, we simplify the expression:

1. Distribute \(3\) in \(3(2x + 1)\): \[ 3(2x + 1) = 6x + 3 \]

2. Now substitute back to the expression: \[ 17x - 10 + 6x + 3 \]

3. Combine like terms: \[ (17x + 6x) + (-10 + 3) = 23x - 7 \]

Thus, the equivalent expression is \(23x - 7\).

2. Simone's Error

Simone correctly identified the factors of \(24\) and \(56\), but she did not use the greatest common factor (GCF) to combine the terms properly.

• The GCF of \(24\) and \(56\) is \(8\), which she used correctly, thus her work appears to be correct based on the factors she listed.

The focal point could be about factors, selection, or operations. Based on the situation you described, the best response might be:

• Simone did not use the correct operations in the equation.

3. Model for Nathaniel's Earnings

To express that "On Wednesday, Nathaniel earned $10 less than he earned on Tuesday," we can represent Nathaniel's earnings on Tuesday as \(n\). Therefore, his earnings on Wednesday would be: \[ n - 10 \] So the correct response is \(n - 10\).

4. Situations for the Expression \(6 - x\)

We need to find which situations correspond to the expression \(6 - x\):

1. Six servings of dinner were decreased by a number. ✓ (This means from the original 6, a number \(x\) servings are removed.)
2. Naomi gives some of her six pencils away. ✓ (Again, this represents her reducing her total of 6 by an unknown amount \(x\).)
3. Westville has 6 fewer schools than Eastville. (This would suggest Eastville has 6 more than Westville, not modeling \(6-x\))
4. Sydney increased her collection of coins by six. (This context does not fit \(6 - x\) since it focuses on an addition, not a subtraction.)
5. Benjamin lost six of his stickers. (This results in a scenario of \(n - 6\), not \(6 - x\))
6. Gabrielle decreased her 6-minute mile by an unknown amount of time. ✓ (This fits \(6 - x\) as well since she is reducing the original time.)

Based on this, the three situations that can represent the expression \(6 - x\) are:

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

Feel free to ask if you need any more assistance!