Solve: `(3)/(4)(x-1)=x-3`. Check the result.

Options

A. x = 11
B. x = 9
C. x = 10
D. x = 12

Answer

To solve the equation \(\frac{3}{4}(x-1) = x - 3\), we will follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 4 to eliminate the fraction.

\[ 4 \cdot \frac{3}{4}(x - 1) = 4 \cdot (x - 3) \]

This simplifies to:

\[ 3(x - 1) = 4(x - 3) \]

### Step 2: Distribute
Now, distribute the 3 on the left side and the 4 on the right side.

\[ 3x - 3 = 4x - 12 \]

### Step 3: Move all terms involving \(x\) to one side
Subtract \(3x\) from both sides to get all \(x\) terms on one side.

\[ -3 = 4x - 3x - 12 \]

This simplifies to:

\[ -3 = x - 12 \]

### Step 4: Isolate \(x\)
Now, add 12 to both sides to isolate \(x\).

\[ -3 + 12 = x \]

This gives us:

\[ x = 9 \]

### Step 5: Check the result
Now, we will substitute \(x = 9\) back into the original equation to verify our solution.

Substituting into the left side:

\[ \frac{3}{4}(9 - 1) = \frac{3}{4}(8) = 6 \]

Substituting into the right side:

\[ 9 - 3 = 6 \]

Since both sides are equal, our solution is verified.

### Final Answer:
\[ x = 9 \]

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