https://file.aiquickdraw.com/mathbot/file/1725768526604o25tx05o.jpg

The image contains the following equation:

\[
\frac{2}{3}y + \frac{5}{6} = \frac{4}{9}y - 2 \frac{1}{3}
\]

It then lists possible values of \( y \):

- (a) \( y = -3 \)
- (b) \( y = 1 \)
- (c) \( y = \frac{7}{9} \)
- (d) \( y = 3 \)

Let me solve the equation step-by-step to find the correct value of \( y \).

The equation is:

\[
\frac{2}{3}y + \frac{5}{6} = \frac{4}{9}y - 2\frac{1}{3}
\]

First, I'll convert all mixed fractions into improper fractions:

\[
2\frac{1}{3} = \frac{7}{3}
\]

The equation becomes:

\[
\frac{2}{3}y + \frac{5}{6} = \frac{4}{9}y - \frac{7}{3}
\]

Next, I'll clear the denominators by multiplying through by the least common denominator (LCD), which is 18.

Let me perform these calculations.The solution to the equation is:

\[
y = -\frac{57}{4}
\]

This value does not match any of the provided options (a, b, c, or d). It seems there may be an error in the options or the problem setup.

Would you like further clarification or details?

Here are some related questions for further exploration:

1. How can you verify the solution of an equation?
2. What is the importance of clearing denominators in fractions during solving?
3. How would the equation change if one of the constants was different?
4. What is the meaning of a solution that doesn't match given options in a multiple-choice context?
5. How does the solution strategy change with higher-order polynomials?

**Tip**: Always double-check your fractions when transforming equations with mixed numbers into improper fractions.

Solve the equation: \( \frac{2}{3}y + \frac{5}{6} = \frac{4}{9}y - 2\frac{1}{3} \). Find the value of \( y \) from the following options: (a) \( y = -3 \), (b) \( y = 1 \), (c) \( y = \frac{7}{9} \), (d) \( y = 3 \).

This page provides a detailed step-by-step solution for solving the linear equation \( \frac{2}{3}y + \frac{5}{6} = \frac{4}{9}y - 2\frac{1}{3} \). It explains the process of converting mixed fractions to improper fractions and clearing denominators. Suitable for students in Grades 6-8.

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