Determine the values of k for which the equation has no solutions: vert 2x+7vert -kleqslant 5 klt -5 kgt 5 klt 5 kgt -5

To determine the values of k for which the equation has no solutions, we need to analyze the given inequality: First, let's isolate the absolute value expression: Now, we need to consider the two cases for the absolute value expression:Case 1: Case 2: For the equation to have no solutions, there should be no values of x that satisfy both cases. This means that the range of x for both cases should not overlap.In Case 1, the range of x is , and in Case 2, the range of x is .For these ranges to not overlap, the value of k must be such that .Therefore, the correct answer is: .