Solve : `x/2+x/4=x/6+7/6`

Answer

To solve the equation \( \frac{x}{2} + \frac{x}{4} = \frac{x}{6} + \frac{7}{6} \), we will follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 2, 4, and 6. The least common multiple (LCM) of these numbers is 12.

### Step 2: Rewrite each term with the common denominator
We will multiply each term by 12 to eliminate the fractions:
\[ 12 \left( \frac{x}{2} \right) + 12 \left( \frac{x}{4} \right) = 12 \left( \frac{x}{6} \right) + 12 \left( \frac{7}{6} \right) \]

### Step 3: Simplify each term
Calculating each term gives:
\[ 6x + 3x = 2x + 14 \]

### Step 4: Combine like terms
Now, combine the terms on the left side:
\[ 9x = 2x + 14 \]

### Step 5: Isolate the variable
To isolate \( x \), subtract \( 2x \) from both sides:
\[ 9x - 2x = 14 \]
\[ 7x = 14 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 7:
\[ x = \frac{14}{7} \]
\[ x = 2 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{2} \]

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