https://file.aiquickdraw.com/mathbot/file/17277903153465wofhpw7.jpg

The equation from the image is:

\[
\frac{1}{12} + \frac{3}{8}y = \frac{5}{12} + \frac{5}{8}y
\]

Let's solve this step by step:

### Step 1: Eliminate the fractions by finding a common denominator
The least common denominator (LCD) of 12 and 8 is 24. Multiply the entire equation by 24 to eliminate the fractions:

\[
24 \left(\frac{1}{12} + \frac{3}{8}y\right) = 24 \left(\frac{5}{12} + \frac{5}{8}y\right)
\]

This simplifies as follows:
\[
2 + 9y = 10 + 15y
\]

### Step 2: Move all terms involving \(y\) to one side
Subtract \(9y\) from both sides:
\[
2 = 10 + 6y
\]

### Step 3: Move constant terms to the other side
Subtract 10 from both sides:
\[
2 - 10 = 6y
\]
\[
-8 = 6y
\]

### Step 4: Solve for \(y\)
Divide both sides by 6:
\[
y = \frac{-8}{6} = \frac{-4}{3}
\]

Thus, the solution is:
\[
y = \frac{-4}{3}
\]

Would you like more details, or do you have any further questions?

Here are some related questions for further practice:
1. How do you find the least common denominator (LCD) for a set of fractions?
2. What other methods can be used to solve equations with fractions?
3. Can you solve a similar equation if one side only has a fraction term, like \( \frac{2}{5}y = \frac{3}{4} \)?
4. How would the process differ if the equation included negative fractions from the start?
5. Can you apply this method to solve systems of equations involving fractions?

**Tip:** When dealing with fractions, clearing them by multiplying through by the least common denominator simplifies the process.

Learn how to solve the linear equation 1/12 + 3/8y = 5/12 + 5/8y by clearing fractions using the least common denominator. Step-by-step explanation and solution for students in Grades 8-10.

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