If x + 1, x-3,x+6 and x are in proportion, then x= _____

Options

A. 9
B. 12
C. 7
D. 4

Explanation

To solve the problem where \( x + 1, x - 3, x + 6, \) and \( x \) are in proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Proportion**:
When four quantities \( a, b, c, d \) are in proportion, it means that the ratio of the first two is equal to the ratio of the last two. Mathematically, this can be expressed as:
\[ \frac{a}{b} = \frac{c}{d} \]
For our case, we have:
\[ \frac{x + 1}{x - 3} = \frac{x + 6}{x} \]

2. **Cross-Multiplication**:
To eliminate the fractions, we can cross-multiply:
\[ (x + 1) \cdot x = (x - 3) \cdot (x + 6) \]

3. **Expanding Both Sides**:
Now, we will expand both sides of the equation:
- Left side:
\[ x(x + 1) = x^2 + x \]
- Right side:
\[ (x - 3)(x + 6) = x^2 + 6x - 3x - 18 = x^2 + 3x - 18 \]

4. **Setting Up the Equation**:
Now we have:
\[ x^2 + x = x^2 + 3x - 18 \]

5. **Simplifying the Equation**:
We can subtract \( x^2 \) from both sides:
\[ x = 3x - 18 \]
Now, rearranging gives:
\[ x - 3x = -18 \]
\[ -2x = -18 \]

6. **Solving for \( x \)**:
Dividing both sides by -2:
\[ x = \frac{-18}{-2} = 9 \]

### Final Answer:
Thus, the value of \( x \) is:
\[ \boxed{9} \]