if (x-1)/(x+1)=7/9,then x=?

Options

A. `6`
B. `7`
C. `8`
D. `10`

Answer

To solve the equation \(\frac{x-1}{x+1} = \frac{7}{9}\), we will follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying to eliminate the fractions. This means we will multiply the numerator of the left side by the denominator of the right side and set it equal to the numerator of the right side multiplied by the denominator of the left side.

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

### Step 2: Distribute
Next, we will distribute both sides of the equation.

On the left side:
\[ 9(x - 1) = 9x - 9 \]

On the right side:
\[ 7(x + 1) = 7x + 7 \]

So, we rewrite the equation as:
\[ 9x - 9 = 7x + 7 \]

### Step 3: Move all terms involving \(x\) to one side
Now, we will move all terms involving \(x\) to one side of the equation and constant terms to the other side. We can do this by subtracting \(7x\) from both sides:

\[ 9x - 7x - 9 = 7 \]

This simplifies to:
\[ 2x - 9 = 7 \]

### Step 4: Move constant terms to the other side
Next, we will add \(9\) to both sides to isolate the term with \(x\):

\[ 2x = 7 + 9 \]

This simplifies to:
\[ 2x = 16 \]

### Step 5: Solve for \(x\)
Finally, we will divide both sides by \(2\) to solve for \(x\):

\[ x = \frac{16}{2} \]

This gives us:
\[ x = 8 \]

### Conclusion
The value of \(x\) is \(8\).

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