If `3j-(k_5)=16-4k`, what is the value of `j+k`?

Options

A. `8`
B. `7`
C. `5`
D. `2`

Answer

To solve the equation \(3j - (k - 5) = 16 - 4k\) and find the value of \(j + k\), we can follow these steps:

### Step 1: Rewrite the equation
Start with the original equation:
\[ 3j - (k - 5) = 16 - 4k \]
Distributing the negative sign in the left side gives:
\[ 3j - k + 5 = 16 - 4k \]

**Hint:** Remember to distribute the negative sign correctly when you have parentheses.

### Step 2: Move all terms involving \(k\) to one side
Next, we want to get all the \(k\) terms on one side and the constant terms on the other side. We can add \(4k\) to both sides and subtract \(5\) from both sides:
\[ 3j - k + 4k = 16 - 5 \]
This simplifies to:
\[ 3j + 3k = 11 \]

**Hint:** When moving terms across the equation, make sure to perform the same operation on both sides to maintain equality.

### Step 3: Factor out the common term
Now we can factor out the common term \(3\) from the left side:
\[ 3(j + k) = 11 \]

**Hint:** Factoring can simplify equations and make it easier to isolate variables.

### Step 4: Solve for \(j + k\)
To find \(j + k\), divide both sides by \(3\):
\[ j + k = \frac{11}{3} \]

**Hint:** When dividing both sides of an equation, ensure you divide each term by the same number.

### Conclusion
Thus, the value of \(j + k\) is \(\frac{11}{3}\).

### Final Answer
The value of \(j + k\) is \(\frac{11}{3}\).