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

Shawana, Dexter, and Tilana are correct.

Given that

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

We have to determine

Which students are correct?

According to the question

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

The correct way to solve the equation is;

SHAWNA

Statement: Dividing each side of the equation by –2.5,

$\rm \dfrac{-2.5(5 - n) + 2 }{-2.5}= \dfrac{15}{-2.5}\\ \\ (5-n) - \dfrac{2}{2.5} = \dfrac{15}{-2.5}$

Here, Shawna is correct.

DEXTER

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

$\rm -2.5(5-n) +2=15\\ \\ -2.5(5) - 2.5 (-n) +2= 15\\ \\ -12.5 +2.5n +2=15$

Hence, Dexter is correct.

" Tirana says, "I can begin by multiplying each side of the equation by Negative Start fraction 1 over 2. 5 End fraction to get 5 minus n minus 0. 8 = negative 6. "

$\rm \dfrac{-1}{2.5} (-2.5 (5-n)+2)= \dfrac{-1}{2.5}\times 15\\ \\ (5-n) + \dfrac{-2}{2.5} = \dfrac{-15}{2.25}\\ \\ (5-n) -\dfrac{2}{2.5} = \dfrac{-15}{2.5}\\ \\ 5-n-0.8=-6$

Hence, Tilana is also correct.

Hence, Shawana, Dexter and Tilana are correct.

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