https://file.aiquickdraw.com/mathbot/file/17257935362731fvtqahs.jpg

The equation in the image is:

\[
\frac{(y + 1) - (2y + 3)}{3 - 2y} = \frac{1}{4}
\]

Let's solve this step by step.

### Step 1: Simplify the numerator
The numerator is \((y + 1) - (2y + 3)\).

Distribute the negative sign:
\[
(y + 1) - (2y + 3) = y + 1 - 2y - 3 = -y - 2
\]

So the equation becomes:
\[
\frac{-y - 2}{3 - 2y} = \frac{1}{4}
\]

### Step 2: Cross multiply
To eliminate the fractions, we cross multiply:
\[
4(-y - 2) = 1(3 - 2y)
\]

This simplifies to:
\[
4(-y - 2) = 3 - 2y
\]
Expanding both sides:
\[
-4y - 8 = 3 - 2y
\]

### Step 3: Move terms involving \(y\) to one side
Add \(4y\) to both sides:
\[
-8 = 3 + 2y
\]

Now subtract 3 from both sides:
\[
-11 = 2y
\]

### Step 4: Solve for \(y\)
Divide both sides by 2:
\[
y = \frac{-11}{2}
\]

Thus, the solution is:
\[
y = -\frac{11}{2}
\]

Would you like further details or explanations on any of the steps?

Here are some related questions:
1. How do you check if a solution satisfies the original equation?
2. What happens if both sides of the equation contain variables in the denominator?
3. Can you generalize the steps for solving fractional equations like this?
4. What are the properties of rational expressions when simplified?
5. How does the cross-multiplication method work in solving equations with fractions?

**Tip**: Always simplify the equation first before applying operations like cross-multiplication. This helps avoid errors in more complex cases.

Solve the equation: \frac{(y + 1) - (2y + 3)}{3 - 2y} = \frac{1}{4}

Learn how to solve the rational equation \frac{(y + 1) - (2y + 3)}{3 - 2y} = \frac{1}{4} using cross-multiplication and simplification. This step-by-step solution demonstrates key algebraic concepts and techniques, suitable for students in Grades 9-11.

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