Question

Shawna, Dexter, and Tilana are solving the equation Negative 2.5 (5 minus n) + 2 = 15. Shawna says, "I can begin by dividing each side of the equation by –2.5 to get 5 minus n minus StartFraction 2 over 2.5 EndFraction = Negative StartFraction 15 over 2.5 EndFraction." Dexter says, "I can begin by distributing Negative 2.5 to get Negative 12.5 + 2.5 n + 2 = 15." Tilana says, "I can begin by multiplying each side of the equation by Negative StartFraction 1 over 2.5 EndFraction to get 5 minus n minus 0.8 = negative 6." Which students are correct? only Shawna and Tilana only Shawna and Dexter only Dexter and Tilana Shawna, Dexter, and Tilana

Answer 1

All of them are correct

Explanation:

Answer 2

All three students are correct

Explanation:

Given

Equation: -2.5(5 - n) + 2 = 15

Required

Which students are correct

To determine which of the students are correct; we have to test each of their solutions

SHAWNA

Statement: Dividing each side of the equation by –2.5 to get 5 - n - 2/2.5 = -15/2.5

`(-2.5(5 - n) + 2)/(-2.5) = (15)/(-2.5)`

Split fractions

`(-2.5(5 - n))/(-2.5) + (2)/(-2.5) = (15)/(-2.5)`

Simplify each fraction

`5-n - (2)/(2.5) = (-15)/(2.5)`

Shawna is correct...

DEXTER

Statement: Distributing -2.5 to get -12.5 + 2.5 n + 2 = 15.

`-2.5(5 - n) + 2 = 15`

Open brackets

`-12.5 + 2.5n + 2 = 15`

Dexter is also correct...

TILANA

`(-1)/(2.5)(-2.5(5 - n) + 2) = (-1)/(2.5) * 15`

Open brackets

`(-1)/(2.5)(-2.5(5 - n)) + (-1)/(2.5)(2) = (-1)/(2.5) * 15`

Simplify each bracket

`(5 - n) + (-2)/(2.5) = (-15)/(2.5)`

`(5 - n) - (2)/(2.5) = (-15)/(2.5)`

`5 - n - 0.8 = -6`

Tilana is also correct

Hence, all three students are correct