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Eliana tried to solve $3.2 + 2(2.4 - 2t) = -16 + t$ . Here is her work: $\newline$ $3.2 + 4.8 - 4t = -16 + t$ {Step $1$ } $\newline$ $8 - 4t = -16 + t$ {Step $2$ } $\newline$ $8 - 3t = -16$ {Step $3$ } $\newline$ $-3t = -24$ {Step $4$ } $\newline$ $t = 8$ {Step $5$ } $\newline$ Did Eliana solve the equation correctly? $\newline$ (A)Yes, Eliana solved the equation correctly. $\newline$ (B)No, Eliana made a mistake in step $1$ . She didn't apply the distributive property correctly. $\newline$ (C)No, Eliana made a mistake in step $3$ . She didn't apply the subtraction property of equality correctly. $\newline$ (D)No, Eliana made a mistake in step $4$ . She didn't apply the division property of equality correctly.

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Add and subtract integers: word problems

Full solution

Q. Eliana tried to solve

3.2 + 2(2.4 - 2t) = -16 + t

. Here is her work:

\newline

3.2 + 4.8 - 4t = -16 + t

{Step

1

}

\newline

8 - 4t = -16 + t

{Step

2

}

\newline

8 - 3t = -16

{Step

3

}

\newline

-3t = -24

{Step

4

}

\newline

t = 8

{Step

5

}

\newline

Did Eliana solve the equation correctly?

\newline

(A)Yes, Eliana solved the equation correctly.

\newline

(B)No, Eliana made a mistake in step

1

. She didn't apply the distributive property correctly.

\newline

(C)No, Eliana made a mistake in step

3

. She didn't apply the subtraction property of equality correctly.

\newline

(D)No, Eliana made a mistake in step

4

. She didn't apply the division property of equality correctly.

Apply Distributive Property: Step $1$ : Apply the distributive property to $2(2.4 - 2t)$ . $\newline$ Calculation: $2 \times 2.4 - 2 \times 2t = 4.8 - 4t$ .
Combine Like Terms: Step $2$ : Combine like terms on the left side of the equation. $\newline$ Calculation: $3.2 + 4.8 - 4t = 8 - 4t$ .
Add and Subtract to Isolate: Step $3$ : Add $t$ to both sides to isolate terms containing $t$ on one side. $\newline$ Calculation: $8 - 4t + t = -16 + t + t$ , which simplifies to $8 - 3t = -16$ .
Divide to Solve for t: Step $4$ : Subtract $8$ from both sides to isolate the terms with $t$ . $\newline$ Calculation: $-3t = -16 - 8$ , which simplifies to $-3t = -24$ .
Divide to Solve for t: Step $4$ : Subtract $8$ from both sides to isolate the terms with $t$ . Calculation: $-3t = -16 - 8$ , which simplifies to $-3t = -24$ . Step $5$ : Divide both sides by $-3$ to solve for $t$ . Calculation: $t = -24 / -3$ , which simplifies to $t = 8$ .

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