If `7/9x- 4/9 x =1/4 + 5/12`, what is the value of x?

Answer

To solve the equation \( \frac{7}{9}x - \frac{4}{9}x = \frac{1}{4} + \frac{5}{12} \), we will follow these steps:

### Step 1: Simplify the left-hand side (LHS)
The left-hand side of the equation is:
\[ \frac{7}{9}x - \frac{4}{9}x \]
We can combine the terms:
\[ \frac{7 - 4}{9}x = \frac{3}{9}x = \frac{1}{3}x \]

### Step 2: Simplify the right-hand side (RHS)
The right-hand side of the equation is:
\[ \frac{1}{4} + \frac{5}{12} \]
To add these fractions, we need a common denominator. The least common multiple (LCM) of 4 and 12 is 12. We convert \( \frac{1}{4} \) to have a denominator of 12:
\[ \frac{1}{4} = \frac{3}{12} \]
Now we can add:
\[ \frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12} \]
We can simplify \( \frac{8}{12} \) to:
\[ \frac{2}{3} \]

### Step 3: Set the simplified LHS equal to the simplified RHS
Now we have:
\[ \frac{1}{3}x = \frac{2}{3} \]

### Step 4: Solve for \( x \)
To isolate \( x \), we can multiply both sides by 3:
\[ x = 2 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{2} \]

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