Question

katarina wrote the standard form of a linear equation as $4x - \frac{2}{3}y = 8$. sofiya told her that the equation was not yet in standard form and gave her the right advice for how to fix it. what advice did sofiya give to katarina?\
\bigcirc\\ multiply both sides of the equation by 3. the standard form of the equation is $12x - 2y = 24$.\
\bigcirc\\ multiply both sides of the equation by 3 and then divide both sides by 2. the standard form of the equation is $6x - y = 12$.\
\bigcirc\\ multiply both sides of the equation by 3. the standard form of the equation is $12x - 2y = 8$.\
\bigcirc\\ multiply both sides of the equation by 3 and then divide both sides by 2. the standard form of the equation is $6x - y = 4$.

Explanation:

Step1: Recall Standard Form

The standard form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers, and \(A\) is non - negative. The given equation is \(4x-\frac{2}{3}y = 8\). To eliminate the fraction, we multiply both sides of the equation by the denominator of the fraction, which is 3.

Step2: Multiply by 3

Multiply each term in the equation \(4x-\frac{2}{3}y = 8\) by 3.
For the first term: \(3\times4x=12x\)
For the second term: \(3\times(-\frac{2}{3}y)=- 2y\)
For the third term: \(3\times8 = 24\)
So the equation becomes \(12x-2y=24\) after multiplying both sides by 3.

Answer:

Multiply both sides of the equation by 3. The standard form of the equation is \(12x - 2y=24\). (The first option)