`(7-(4-q))/8=(3(5-q))/12`
In the equation above, what is the value of q?

Answer

To solve the equation \( \frac{7 - (4 - q)}{8} = \frac{3(5 - q)}{12} \), we will follow these steps:

### Step 1: Simplify both sides of the equation
First, let's rewrite the equation for clarity:

\[ \frac{7 - (4 - q)}{8} = \frac{3(5 - q)}{12} \]

### Step 2: Eliminate the denominators
To eliminate the fractions, we can cross-multiply. The left side will be multiplied by 12 and the right side by 8:

\[ 12(7 - (4 - q)) = 8(3(5 - q)) \]

### Step 3: Distribute on both sides
Now, we will distribute on both sides:

Left side:
\[ 12(7 - 4 + q) = 12(3 + q) = 84 + 12q \]

Right side:
\[ 8(15 - 3q) = 120 - 24q \]

So, we have:

\[ 84 + 12q = 120 - 24q \]

### Step 4: Move all terms involving \(q\) to one side
Now, let's move all terms involving \(q\) to one side and constants to the other side:

\[ 12q + 24q = 120 - 84 \]

This simplifies to:

\[ 36q = 36 \]

### Step 5: Solve for \(q\)
Now, divide both sides by 36:

\[ q = \frac{36}{36} = 1 \]

### Final Answer
The value of \(q\) is \(1\).

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