`(5)/(8)=(-(11-7y))/(4y)+(1)/(2y)-(1)/(8)`
What value of makes the equation above a true statement?

Answer

To solve the equation

\[ \frac{5}{8} = \frac{-(11 - 7y)}{4y} + \frac{1}{2y} - \frac{1}{8} \]

we will follow these steps:

### Step 1: Rewrite the equation
The equation is already given in a suitable form. We will work with it as it is.

### Step 2: Find a common denominator
The denominators in the right-hand side are \(4y\), \(2y\), and \(8\). The least common multiple (LCM) of these denominators is \(8y\).

### Step 3: Rewrite each term with the common denominator
We will rewrite each term on the right-hand side with the common denominator \(8y\):

1. The first term:
\[ \frac{-(11 - 7y)}{4y} = \frac{-2(11 - 7y)}{8y} = \frac{-22 + 14y}{8y} \]

2. The second term:
\[ \frac{1}{2y} = \frac{4}{8y} \]

3. The third term:
\[ -\frac{1}{8} = -\frac{y}{8y} \]

Now, we can combine these terms:
\[ \frac{-22 + 14y + 4 - y}{8y} = \frac{(14y - y - 22 + 4)}{8y} = \frac{13y - 18}{8y} \]

### Step 4: Set the equation
Now we have:
\[ \frac{5}{8} = \frac{13y - 18}{8y} \]

### Step 5: Cross-multiply
Cross-multiplying gives us:
\[ 5 \cdot 8y = 8(13y - 18) \]
This simplifies to:
\[ 40y = 104y - 144 \]

### Step 6: Rearrange the equation
Now, we will rearrange the equation:
\[ 40y - 104y = -144 \]
\[ -64y = -144 \]

### Step 7: Solve for \(y\)
Dividing both sides by \(-64\):
\[ y = \frac{-144}{-64} = \frac{144}{64} = \frac{9}{4} \]

### Final Answer
Thus, the value of \(y\) that makes the equation true is:
\[ y = \frac{9}{4} \]

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