Let's evaluate each statement about the equation \( 2x - 5 = 8 + x \):
Statement #1: There are two constants in the equation.
- In this equation, the constants are \(-5\) and \(8\). So, there are indeed two constants. This statement is correct.
Statement #2: x does not have a coefficient.
- In the equation, \(2x\) has a coefficient of \(2\) and \(x\) has a coefficient of \(1\) (implied). Therefore, this statement is incorrect.
Statement #3: There are two terms in the equation.
- The left side of the equation \(2x - 5\) has two terms: \(2x\) and \(-5\). The right side \(8 + x\) also has two terms: \(8\) and \(x\). However, if we consider the entire equation \( 2x - 5 = 8 + x \), it has four terms (two on each side). Given that "terms" is typically understood as "individual parts of the equation," this statement is incorrect.
In conclusion, the only correct statement is Statement #1. Therefore, the correct answer is Statement #1 is correct.