Solve the inequalities:

Question

(1). 3 sin2x > sinx + cosx + 1

(2). √(x-5) -√(9-x) ≥1

(3). log_x⁡〖(4x+5)/(6-5x)〗 < -1?

Answer 1

(2).

The radical inequality is .

Since the radicand of a square root must be greater than or equal to equal to zero, first solve to identify the values of x for which the left side of the given inequality is defined.

.

It appears that .

Here two solutions :

.

.

The solution set is .

Answer 2

(3).

The inequality is .