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Leo tried to solve $-\frac{3}{4}(7z - 4) = \frac{1}{4}(4 + 3z)$ . Here is his work: $\newline$ $-\frac{21}{4}z + 3 = 1 + \frac{3}{4}z$ {Step $1$ } $\newline$ $-6z + 3 = 1$ {Step $2$ } $\newline$ $-6z = -2$ {Step $3$ } $\newline$ $z = 3$ {Step $4$ } $\newline$ Did Leo solve the equation correctly? $\newline$ (A) Yes, Leo solved the equation correctly. $\newline$ (B) No, Leo made a mistake in step $1$ . He didn't apply the distributive property correctly. $\newline$ (C) No, Leo made a mistake in step $2$ . He didn't apply the subtraction property of equality correctly. $\newline$ (D) No, Leo made a mistake in step $4$ . He didn't apply the division property of equality correctly.

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Add and subtract integers: word problems

Full solution

Q. Leo tried to solve

-\frac{3}{4}(7z - 4) = \frac{1}{4}(4 + 3z)

. Here is his work:

\newline

-\frac{21}{4}z + 3 = 1 + \frac{3}{4}z

{Step

1

}

\newline

-6z + 3 = 1

{Step

2

}

\newline

-6z = -2

{Step

3

}

\newline

z = 3

{Step

4

}

\newline

Did Leo solve the equation correctly?

\newline

(A) Yes, Leo solved the equation correctly.

\newline

(B) No, Leo made a mistake in step

1

. He didn't apply the distributive property correctly.

\newline

(C) No, Leo made a mistake in step

2

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

\newline

(D) No, Leo made a mistake in step

4

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

Apply distributive property: Step $1$ : Apply the distributive property to both sides of the equation. $\newline$ $-\frac{3}{4} \times 7z + -\frac{3}{4} \times -4 = \frac{1}{4} \times 4 + \frac{1}{4} \times 3z$ $\newline$ $-\frac{21}{4}z + 3 = 1 + \frac{3}{4}z$
Combine like terms: Step $2$ : Combine like terms and simplify the equation. $\newline$ Add $-\frac{3}{4}z$ from the right side to the left side to isolate terms involving $z$ . $\newline$ $-\frac{21}{4}z - \frac{3}{4}z = 1 - 3$ $\newline$ $-\frac{24}{4}z = -2$ $\newline$ $-6z = -2$
Solve for z: Step $3$ : Solve for z by dividing both sides by $-6$ . $\newline$ $z = \frac{-2}{-6}$ $\newline$ $z = \frac{1}{3}$

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