To solve the equation \( 14 + 3x = -(2 + 14x) \), follow these steps:

### Step 1: Distribute the negative sign on the right side of the equation.
\[
14 + 3x = -2 - 14x
\]

### Step 2: Move the terms involving \( x \) to one side of the equation.
Add \( 14x \) to both sides:
\[
14 + 3x + 14x = -2 - 14x + 14x
\]
\[
14 + 17x = -2
\]

### Step 3: Move the constant term to the other side.
Subtract 14 from both sides:
\[
17x = -2 - 14
\]
\[
17x = -16
\]

### Step 4: Solve for \( x \) by dividing both sides by 17:
\[
x = \frac{-16}{17}
\]

So, the solution is:
\[
x = -\frac{16}{17}
\]

Would you like more details or have any questions about the steps? 

Here are 5 related questions:
1. How would you check if \( x = -\frac{16}{17} \) is correct?
2. What happens if you add \( x \) to both sides instead of moving \( x \) to one side?
3. How can you express the solution in decimal form?
4. What if the equation had been \( 14 + 3x = -2(1 + 7x) \)?
5. Can you generalize the method used to solve equations of this type?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the equation 14 + 3x = -(2 + 14x) with a detailed step-by-step solution. This problem covers linear equations, the distributive property, and solving equations involving variables on both sides. Suitable for students in Grades 7-9.

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