Solve the following equations :
`(x+2)/(9)=(x+4)/(11)`

Answer

To solve the equation \(\frac{x+2}{9} = \frac{x+4}{11}\), we can follow these steps:

### Step 1: Cross-multiply the fractions
To eliminate the denominators, we can cross-multiply:
\[ (x + 2) \cdot 11 = (x + 4) \cdot 9 \]

### Step 2: Expand both sides
Now, we will expand both sides of the equation:
\[ 11(x + 2) = 9(x + 4) \]
This gives us:
\[ 11x + 22 = 9x + 36 \]

### Step 3: Move all \(x\) terms to one side
Next, we will move all terms involving \(x\) to the left side and constant terms to the right side. We can subtract \(9x\) from both sides:
\[ 11x - 9x + 22 = 36 \]
This simplifies to:
\[ 2x + 22 = 36 \]

### Step 4: Move constant terms to the right side
Now, we will subtract \(22\) from both sides:
\[ 2x = 36 - 22 \]
This simplifies to:
\[ 2x = 14 \]

### Step 5: Solve for \(x\)
Finally, we will divide both sides by \(2\) to solve for \(x\):
\[ x = \frac{14}{2} \]
This gives us:
\[ x = 7 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{7} \]

---