Question

What step can be taken to change the equation
2
1

x+2y=12 to standard form?

Multiply all terms by −2.

Multiply all terms by
2
1

.

Multiply all terms by 2.

None of these steps can be taken.

Answers

GPT-4o mini
To convert the equation \( \frac{1}{2}x + 2y = 12 \) to standard form, we want to eliminate any fractions.

Among the options provided, the correct step would be to **multiply all terms by 2**. Here’s how that would look:

1. Start with the original equation:
\[
\frac{1}{2}x + 2y = 12
\]
2. Multiply every term by 2:
\[
2 \cdot \left(\frac{1}{2}x\right) + 2 \cdot (2y) = 2 \cdot 12
\]
Which simplifies to:
\[
x + 4y = 24
\]

Now the equation is in standard form \( Ax + By = C \).

So, the choice is: **Multiply all terms by 2.**

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