Solve for `x.(x)/(3)-(4)/(9)=(8)/(9)`

Answer

To solve the equation \(\frac{x}{3} - \frac{4}{9} = \frac{8}{9}\), we will follow these steps:

### Step 1: Eliminate the Denominators
To eliminate the fractions, we can multiply the entire equation by 9, which is the least common multiple of the denominators (3 and 9).

\[ 9 \left(\frac{x}{3}\right) - 9 \left(\frac{4}{9}\right) = 9 \left(\frac{8}{9}\right) \]

### Step 2: Simplify Each Term
Now, we simplify each term:

\[ \frac{9x}{3} - 4 = 8 \]

Since \( \frac{9}{3} = 3\), we can rewrite the equation as:

\[ 3x - 4 = 8 \]

### Step 3: Isolate the Variable
Next, we want to isolate \(x\). To do this, we will add 4 to both sides of the equation:

\[ 3x - 4 + 4 = 8 + 4 \]

This simplifies to:

\[ 3x = 12 \]

### Step 4: Solve for \(x\)
Now, we will divide both sides by 3 to solve for \(x\):

\[ x = \frac{12}{3} \]

This simplifies to:

\[ x = 4 \]

### Final Answer
Thus, the solution to the equation is:

\[ \boxed{4} \]

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