A single variable linear equation can contain:
- one solution: This occurs when the equation represents a line that intersects the x-axis at a single point.
- no solution: This occurs when the equation represents a contradiction (for example, \(x = 3\) and \(x = 5\) simultaneously).
- infinite number of solutions: This occurs when the equation simplifies to a tautology (for example, \(0 = 0\) after simplification).
However, a single variable linear equation cannot contain two solutions because a linear equation in one variable represents a straight line, which can intersect a point at most once.
So the correct selections are:
- one solution
- no solution
- infinite number of solutions