https://file.aiquickdraw.com/mathbot/file/1726573922717d7bza2xz.jpg

The equation in the image is:

\[
\frac{1}{2}x + 5 = \frac{2}{3}y + 6
\]

To write this equation in standard form, we want to move all variables to one side and the constants to the other. Here's how we can do that:

### Step-by-step process:
1. Start with the given equation:
   \[
   \frac{1}{2}x + 5 = \frac{2}{3}y + 6
   \]

2. Subtract \(\frac{2}{3}y\) from both sides to move the \(y\)-term to the left side:
   \[
   \frac{1}{2}x - \frac{2}{3}y + 5 = 6
   \]

3. Subtract 5 from both sides to isolate the constants:
   \[
   \frac{1}{2}x - \frac{2}{3}y = 6 - 5
   \]
   Simplifying the right side:
   \[
   \frac{1}{2}x - \frac{2}{3}y = 1
   \]

4. To eliminate the fractions, multiply the entire equation by the least common denominator (LCD) of 2 and 3, which is 6:
   \[
   6\left(\frac{1}{2}x - \frac{2}{3}y\right) = 6 \times 1
   \]

5. Distribute the 6:
   \[
   3x - 4y = 6
   \]

This is the equation in **standard form**: 

\[
3x - 4y = 6
\]

Would you like more details on any of the steps, or have any questions?

Here are 5 related questions to practice:
1. How do you find the least common denominator of two fractions?
2. Can you solve the equation for \(x\) in terms of \(y\) instead?
3. What is the slope-intercept form of this equation?
4. How do you solve systems of equations using substitution?
5. What does the standard form of a linear equation represent geometrically?

**Tip:** Always eliminate fractions in an equation by multiplying through by the least common denominator to make the equation easier to work with!

Write the equation 1/2x + 5 = 2/3y + 6 in standard form.

Learn how to transform the equation 1/2x + 5 = 2/3y + 6 into its standard form, 3x - 4y = 6. This step-by-step solution is suitable for students in Grades 8-10 and covers key algebraic concepts, such as handling fractions and rearranging equations.

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