Question

type your response in the box.
grace, chelsea, and roan are simplifying the same polynomial expression. which student’s work is correct and why?
grace: 3(2 - x) - 2(6x - 8) = 6 - 3x - 12x + 16 = -3x - 12x + 16 + 6 = -15x + 22
chelsea: 3(2 - x) - 2(6x - 8) = 6 - 3x - 12x - 16 = -3x - 12x - 16 + 6 = -15x - 10
roan: 3(2 - x) - 2(6x - 8) = 6 - 3x + 12x - 16 = -3x + 12x - 16 + 6 = 9x - 10

Explanation:

Step1: Apply distributive property

Original expression: $3(2 - x) - 2(6x - 8)$
Correct distribution: $3*2 - 3*x - 2*6x + (-2)*(-8) = 6 - 3x -12x +16$
Grace did this correctly; Chelsea used $-16$ (wrong sign), Roan used $+12x$ (wrong sign).

Step2: Combine like terms

Grace: $-3x -12x +16 +6 = -15x +22$ (correct)
Chelsea: $-15x -10$ (wrong constant term), Roan: $9x -10$ (wrong x coefficient).

Answer:

Grace's work is correct because she properly applied the distributive property (maintaining the positive sign when multiplying -2 by -8) and combined like terms accurately. The final simplified form is $-15x + 22$.