Katarina wrote the standard form of a linear equation as 4x – 4 x minus StartFraction 2 Over 3 EndFraction y equals 8.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?

Question

Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 24.
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.
Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 8.
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.

Answer 1

To convert Katarina's equation \(4x - \frac{2}{3}y = 8\) into standard form, we need the equation to be in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers and \(A\) is non-negative.

Currently, the equation has a fraction, which is why it's not in standard form. To eliminate the fraction, Sofiya correctly suggests multiplying both sides of the equation by 3:

\[ 3(4x - \frac{2}{3}y) = 3(8) \]

This simplifies to:

\[ 12x - 2y = 24 \]

Now, \(12x - 2y = 24\) is indeed in standard form. So, the correct advice that Sofiya gave to Katarina is:

Multiply both sides of the equation by 3. The standard form of the equation is 12x – 2y = 24.