Let's solve the equation \( 14 - 2k = 5(1 - k) \) step by step.

### Step 1: Expand the right-hand side.
Distribute the \( 5 \) on the right side:
\[
5(1 - k) = 5 \times 1 - 5 \times k = 5 - 5k
\]
Now the equation becomes:
\[
14 - 2k = 5 - 5k
\]

### Step 2: Move all terms with \( k \) to one side.
Add \( 5k \) to both sides to eliminate \( -5k \) from the right side:
\[
14 - 2k + 5k = 5
\]
Simplifying:
\[
14 + 3k = 5
\]

### Step 3: Move constant terms to the other side.
Subtract 14 from both sides to move constants to the right side:
\[
3k = 5 - 14
\]
Simplifying:
\[
3k = -9
\]

### Step 4: Solve for \( k \).
Divide both sides by 3:
\[
k = \frac{-9}{3} = -3
\]

### Final Answer:
\[
k = -3
\]

Would you like more details on any of the steps? 

Here are 5 related questions to explore:
1. What happens if you add \( 2k \) to both sides instead of adding \( 5k \)?
2. How do you solve a similar equation if it has fractions?
3. Can you solve \( 14 - 2k = 5k + 1 \) and compare the solutions?
4. What happens if the equation was \( 14 - 2k = 5(k - 1) \)?
5. How can you check your solution by plugging \( k = -3 \) back into the original equation?

**Tip**: Always verify your solution by substituting it back into the original equation!

Learn how to solve the linear equation 14 - 2k = 5(1 - k) using algebraic techniques such as the distributive property and combining like terms. This step-by-step solution is ideal for students in Grades 7-9.

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