`(4x+7)/(9-3x)=1/4`

Options

A. `-3`
B. `0`
C. `2`
D. `-1`

Answer

To solve the equation \((4x + 7)/(9 - 3x) = 1/4\), we will follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying to eliminate the fraction. This means we multiply both sides of the equation by the denominators:

\[ 4(4x + 7) = 1(9 - 3x) \]

### Step 2: Distribute
Next, we distribute the numbers on both sides:

\[ 16x + 28 = 9 - 3x \]

### Step 3: Move all terms involving \(x\) to one side
Now, we will move the \(3x\) term from the right side to the left side by adding \(3x\) to both sides:

\[ 16x + 3x + 28 = 9 \]

This simplifies to:

\[ 19x + 28 = 9 \]

### Step 4: Move constant terms to the other side
Next, we will isolate the \(x\) term by moving the constant \(28\) to the right side. We do this by subtracting \(28\) from both sides:

\[ 19x = 9 - 28 \]

This simplifies to:

\[ 19x = -19 \]

### Step 5: Solve for \(x\)
Finally, we divide both sides by \(19\) to solve for \(x\):

\[ x = \frac{-19}{19} \]

This simplifies to:

\[ x = -1 \]

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

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