y-(y-1/2) = (y-2/3)-y+4   (y-1/2 are on the same fractional bar. Same with y-2/3)

The given equation is:

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

Let's simplify this step by step:

### Step 1: Simplify the left-hand side (LHS)
\[
y - \frac{y - \frac{1}{2}}{1} = y - \left( y - \frac{1}{2} \right) = y - y + \frac{1}{2} = \frac{1}{2}
\]
So, the left-hand side becomes:
\[
\frac{1}{2}
\]

### Step 2: Simplify the right-hand side (RHS)
\[
\frac{y - \frac{2}{3}}{1} - y + 4 = (y - \frac{2}{3}) - y + 4
\]
Now, distribute and simplify:
\[
y - \frac{2}{3} - y + 4 = -\frac{2}{3} + 4 = \frac{10}{3}
\]
So, the right-hand side becomes:
\[
\frac{10}{3}
\]

### Step 3: Set the simplified LHS equal to the simplified RHS
\[
\frac{1}{2} = \frac{10}{3}
\]

This is clearly a contradiction, as \(\frac{1}{2} \neq \frac{10}{3}\). Therefore, **there is no solution** to this equation.

Would you like further clarification or more details?

Here are 5 related questions you might explore:
1. How do you solve equations involving fractional expressions?
2. What methods can be used to verify if an equation has no solution?
3. How do you handle contradictions in algebraic equations?
4. Can you graphically represent why this equation has no solution?
5. What are some real-world applications where equations have no solutions?

**Tip:** Always simplify both sides of an equation step by step to avoid errors.

y - (y - 1/2) = (y - 2/3) - y + 4 (Note: y - 1/2 and y - 2/3 are both fractional expressions)

This page provides a step-by-step solution to the algebraic equation involving fractions: y - (y - 1/2) = (y - 2/3) - y + 4. It simplifies both sides of the equation, identifies contradictions, and concludes that there is no solution. Ideal for students in Grades 9-10 looking to master equation solving with fractions.

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