https://file.aiquickdraw.com/mathbot/file/1726777701106hsde81rf.jpg

The equation provided in the image is:

\[
\frac{5y - 3}{5} + \frac{16}{10} = \frac{10y + 4}{10}
\]

Let's solve this step-by-step:

### Step 1: Eliminate the denominators by multiplying the entire equation by 10 (the least common denominator of 5 and 10).

\[
10 \times \left( \frac{5y - 3}{5} + \frac{16}{10} \right) = 10 \times \frac{10y + 4}{10}
\]

This simplifies to:

\[
2(5y - 3) + 16 = 10y + 4
\]

### Step 2: Expand both sides.

\[
2(5y - 3) = 10y - 6
\]
So the equation becomes:

\[
10y - 6 + 16 = 10y + 4
\]

### Step 3: Simplify the equation.

\[
10y + 10 = 10y + 4
\]

### Step 4: Subtract \(10y\) from both sides.

\[
10 = 4
\]

This is a contradiction, meaning that there is no solution to this equation. The original equation is inconsistent.

---

Would you like more details on how to handle similar equations or explore a different topic?

### Related questions:
1. How do you handle equations with fractions differently?
2. What are some other examples of inconsistent equations?
3. How do you know when an equation has no solution?
4. Can there be cases where equations like this have infinite solutions?
5. What happens if the variables cancel out on both sides?

### Tip:
When solving equations with fractions, it's often helpful to clear the fractions early by multiplying through by the least common denominator (LCD). This simplifies the equation and makes it easier to handle.

Solve the equation (5y - 3)/5 + 16/10 = (10y + 4)/10.

Learn how to solve the linear equation with fractions: (5y - 3)/5 + 16/10 = (10y + 4)/10. This solution demonstrates the use of multiplication to eliminate denominators and simplifies the equation step-by-step. Suitable for students in Grades 8-10.

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