`(4(d+3)-9)/(8)=(10-(2-d))/(6)`
In the equation above, what is the value of a?

Options

A. `(23)/(16)`
B. `(23)/(8)`
C. `(25)/(8)`
D. `(25)/(4)`

Answer

To solve the equation \((4(d+3)-9)/(8)=(10-(2-d))/(6)\), we will follow these steps:

### Step 1: Simplify both sides of the equation
Start by simplifying the left side:
\[ \frac{4(d + 3) - 9}{8} \]
Distributing \(4\) inside the parentheses:
\[ = \frac{4d + 12 - 9}{8} = \frac{4d + 3}{8} \]

Now simplify the right side:
\[ \frac{10 - (2 - d)}{6} \]
Distributing the negative sign:
\[ = \frac{10 - 2 + d}{6} = \frac{8 + d}{6} \]

Now we have the equation:
\[ \frac{4d + 3}{8} = \frac{8 + d}{6} \]

### Step 2: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ 6(4d + 3) = 8(8 + d) \]

### Step 3: Distribute on both sides
Distributing on the left side:
\[ 24d + 18 \]
Distributing on the right side:
\[ 64 + 8d \]

So the equation now looks like:
\[ 24d + 18 = 64 + 8d \]

### Step 4: Move all terms involving \(d\) to one side and constant terms to the other side
Subtract \(8d\) from both sides:
\[ 24d - 8d + 18 = 64 \]
This simplifies to:
\[ 16d + 18 = 64 \]

Now, subtract \(18\) from both sides:
\[ 16d = 64 - 18 \]
This simplifies to:
\[ 16d = 46 \]

### Step 5: Solve for \(d\)
Now divide both sides by \(16\):
\[ d = \frac{46}{16} = \frac{23}{8} \]

Thus, the value of \(d\) is:
\[ \boxed{\frac{23}{8}} \]

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