Which option gives the correct interval form of \(x>-6\)?

Correct answer: ((-6,\infty))

The direct answer is option C: \((-6,\infty)\). The inequality \(x>-6\) includes every real number greater than \(-6\), but it does not include \(-6\) itself. In interval notation, an excluded finite endpoint uses a round parenthesis, so the left side is \((-6\). The values continue without an upper limit, represented by \(\infty\), and infinity always uses a round parenthesis because it is not an actual number. Hence the interval is \((-6,\infty)\). Option A, \([-6,\infty)\), wrongly includes \(-6\). Option B, \((-\infty,-6)\), describes numbers less than \(-6\), so it points in the opposite direction. Option C correctly describes all numbers greater than \(-6\). Option D, \((-\infty,-6]\), also describes the wrong side and includes \(-6\). For a quick check, 0 belongs because \(0>-6\), while \(-7\) does not. Memory cue: greater than means move right; strict inequalities use an open endpoint.