Let's solve each equation step by step.

### First Equation: \( 12 + x = 5 - 13x \)

1. Combine like terms involving \( x \):
   \[ 12 + x + 13x = 5 \]
   \[ 12 + 14x = 5 \]

2. Isolate \( x \):
   \[ 14x = 5 - 12 \]
   \[ 14x = -7 \]

3. Solve for \( x \):
   \[ x = \frac{-7}{14} \]
   \[ x = -\frac{1}{2} \]

So, the solution for the first equation is \( x = -\frac{1}{2} \).

### Second Equation: \( 7x - 8 = 3x + 2 \)

1. Combine like terms involving \( x \):
   \[ 7x - 3x = 2 + 8 \]
   \[ 4x = 10 \]

2. Solve for \( x \):
   \[ x = \frac{10}{4} \]
   \[ x = \frac{5}{2} \]

So, the solution for the second equation is \( x = \frac{5}{2} \).

### Summary:
- For the first equation \( 12 + x = 5 - 13x \), the solution is \( x = -\frac{1}{2} \).
- For the second equation \( 7x - 8 = 3x + 2 \), the solution is \( x = \frac{5}{2} \).

Would you like any more details or have any questions?

Here are 5 questions you might ask next:
1. How do you solve quadratic equations?
2. Can you explain how to factor polynomials?
3. What are the steps to solve a system of linear equations?
4. How do you solve inequalities involving absolute values?
5. What is the process for solving exponential equations?

**Tip:** Always check your solutions by substituting them back into the original equations to ensure they satisfy the equations.

Learn how to solve linear equations 12 + x = 5 - 13x and 7x - 8 = 3x + 2 with detailed step-by-step solutions. This problem covers key algebraic concepts, including solving linear equations and combining like terms. Suitable for students in Grades 7-9.

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