Constructing Equations with Solution x = -2
To create two equations that have the solution \( x = -2 \), we can use the concept of linear equations. Linear equations can be expressed in the form \( ax + b = 0 \), where \( a \) and \( b \) are constants. Here’s how to construct two such equations:

Equation 1: Simple Linear Equation
- Start with the equation:
\( x + 2 = 0 \)
- To isolate \( x \), subtract 2 from both sides:
\( x = -2 \)
- This equation is valid, and its solution is \( x = -2 \).

Equation 2: Modified Linear Equation
- Consider a new equation:
\( 3x + 6 = 0 \)
- Subtract 6 from both sides:
\( 3x = -6 \)
- Now, divide both sides by 3:
\( x = -2 \)
- This equation also has the required solution.

Verification of Solutions
- For the first equation \( x + 2 = 0 \):
- Substitute \( x = -2 \):
\( -2 + 2 = 0 \) (True)
- For the second equation \( 3x + 6 = 0 \):
- Substitute \( x = -2 \):
\( 3(-2) + 6 = 0 \)
\( -6 + 6 = 0 \) (True)

Conclusion
Both equations, \( x + 2 = 0 \) and \( 3x + 6 = 0 \), successfully yield the solution \( x = -2 \). By manipulating basic linear forms, we can create various equations with the same solution.