`(k)/(6)+(3(1-k))/(4)=(k-5)/(2)`
What is the solution for k in the equation above?

Answer

To solve the equation \(\frac{k}{6} + \frac{3(1-k)}{4} = \frac{k-5}{2}\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can find a common denominator for all the terms. The denominators are 6, 4, and 2. The least common multiple (LCM) of these numbers is 12. We will multiply every term by 12.

\[ 12 \left(\frac{k}{6}\right) + 12 \left(\frac{3(1-k)}{4}\right) = 12 \left(\frac{k-5}{2}\right) \]

### Step 2: Simplify each term
Now we simplify each term:

\[ 2k + 9(1-k) = 6(k-5) \]

### Step 3: Distribute
Next, we distribute the terms:

\[ 2k + 9 - 9k = 6k - 30 \]

### Step 4: Combine like terms
Now, we combine like terms on the left side:

\[ -7k + 9 = 6k - 30 \]

### Step 5: Move all \(k\) terms to one side
We will move all terms involving \(k\) to one side and constant terms to the other side:

\[ 9 + 30 = 6k + 7k \]

This simplifies to:

\[ 39 = 13k \]

### Step 6: Solve for \(k\)
Now, we divide both sides by 13 to isolate \(k\):

\[ k = \frac{39}{13} = 3 \]

Thus, the solution for \(k\) is:

\[ \boxed{3} \]

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