Let's analyze the equation \( 2x - 5 = 8 + x \) and the statements:
Statement #1: There are two constants in the equation.
- In the equation, the constants are -5 and 8. This statement is correct because there are indeed two constants.
Statement #2: x does not have a coefficient.
- In the equation, \( x \) has an implicit coefficient of 1 (in front of the \( x \) on the right side). Therefore, this statement is incorrect.
Statement #3: There are two terms in the equation.
- The left side has the terms \( 2x \) and \(-5\) (so 2 terms), and the right side has \(8\) and \( x \) (so 2 terms). Thus, the entire equation has 4 terms in total. This statement is incorrect.
Based on this analysis, the correct statement is Statement #1.
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