Solve the equations and check your answer in the case:
`(x)/(3)+(x)/(4)=14`

Answer

To solve the equation \(\frac{x}{3} + \frac{x}{4} = 14\), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
The denominators in the equation are 3 and 4. The LCM of 3 and 4 is 12.

### Step 2: Rewrite the equation with the LCM
We will multiply each term in the equation by 12 to eliminate the denominators:
\[ 12 \left(\frac{x}{3}\right) + 12 \left(\frac{x}{4}\right) = 12 \cdot 14 \]

### Step 3: Simplify the equation
This gives us:
\[ 4x + 3x = 168 \]

### Step 4: Combine like terms
Now combine the terms on the left side:
\[ 7x = 168 \]

### Step 5: Solve for \(x\)
To find \(x\), divide both sides by 7:
\[ x = \frac{168}{7} \]
Calculating this gives:
\[ x = 24 \]

### Step 6: Verification
To verify our solution, substitute \(x = 24\) back into the original equation:
\[ \frac{24}{3} + \frac{24}{4} \]
Calculating each term:
\[ 8 + 6 = 14 \]
Since the left-hand side (LHS) equals the right-hand side (RHS), we have:
\[ LHS = RHS = 14 \]
Thus, the solution is verified.

### Final Answer
The solution to the equation \(\frac{x}{3} + \frac{x}{4} = 14\) is:
\[ x = 24 \]