`(a)/(3)=(b)/(3)=(c )/(2)=(a+b+2c)/(x)`
find `x=?`

Answer

To solve the equation \(\frac{a}{3} = \frac{b}{3} = \frac{c}{2} = \frac{a+b+2c}{x}\), we can follow these steps:

### Step 1: Set the common ratio
Let us denote the common ratio by \(k\). Therefore, we can express \(a\), \(b\), and \(c\) in terms of \(k\):
\[ \frac{a}{3} = k \implies a = 3k \]
\[ \frac{b}{3} = k \implies b = 3k \]
\[ \frac{c}{2} = k \implies c = 2k \]

### Step 2: Substitute \(a\), \(b\), and \(c\) into the equation
Now we substitute \(a\), \(b\), and \(c\) into the equation \(\frac{a+b+2c}{x} = k\):
\[ \frac{3k + 3k + 2(2k)}{x} = k \]

### Step 3: Simplify the numerator
Now simplify the numerator:
\[ 3k + 3k + 4k = 10k \]
So, we have:
\[ \frac{10k}{x} = k \]

### Step 4: Cross-multiply to solve for \(x\)
Cross-multiplying gives:
\[ 10k = kx \]

### Step 5: Divide by \(k\) (assuming \(k \neq 0\))
Assuming \(k \neq 0\), we can divide both sides by \(k\):
\[ 10 = x \]

### Step 6: Conclusion
Thus, the value of \(x\) is:
\[ \boxed{10} \]