Which expression is equivalent to 17x+10−3(2x+1)17x+10−3(2x+1) ?(1 point) Responses 11x−911x−911 x minus 9 23x−923x−923 x minus 9 11x+711x+711 x plus 7 23x−7

Simone applied the distributive property using the greatest common factor to determine the expression that is equivalent to 28+6028+60 . Her work is shown below. Factors of 24: 1, 2, 4, 7, 14, 28 Factors of 56: 1, 2, 3, 4, 5, 6, 10, 15, 20, 30, 60 28+60=4(7+20)28+60=4(7+20) 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 60 in the equation. Simone did not use the correct factors for 60 in the equation. Simone did not use the correct operations in the equation. Simone did not use the correct operations in the equation. Simone did not use the correct factors for 28 in the equation.
Which expression can be used to model the statement, "On Wednesday, Nathaniel earned $10 more than he earned on Tuesday"?(1 point) Responses n−10n−10n minus 10 10>n10>n10 is greater than n n+10n+10n plus 10 10n

1 answer

Let's break down each question one by one:

  1. Expression Equivalent to 17x + 10 - 3(2x + 1): We start by applying the distributive property to the expression \( -3(2x + 1) \): \[ -3(2x + 1) = -6x - 3 \] Now, substituting back into the expression: \[ 17x + 10 - 6x - 3 \] Combine like terms: \[ (17x - 6x) + (10 - 3) = 11x + 7 \] Therefore, the equivalent expression is: 11x + 7

  2. Simone's Error: According to what was presented: Simone says that \( 28 + 60 = 4(7 + 20) \). To use the greatest common factor correctly, she should have correctly identified the factors of 28 and 60. The GCF of 28 and 60 is actually 4. She used "7" and "20" as factors for \( 28 \) and \( 60 \) respectively, which is incorrect since she has mixed them up. Therefore, the best statement describing her error is: Simone did not use the correct factors for 60 in the equation.

  3. Expression for "On Wednesday, Nathaniel earned $10 more than he earned on Tuesday": If we represent Nathaniel’s earnings on Tuesday as \( n \), then his earnings on Wednesday would be \( n + 10 \) because he earned $10 more on that day. Therefore, the correct expression to model the situation is: n + 10

In summary:

  1. 11x + 7
  2. Simone did not use the correct factors for 60 in the equation.
  3. n + 10