`arctan(2x-5) = -1` Solve the equation for x

The range of arctan function is `(-pi/2, pi/2),` on which interval tangent function is strictly monotone. Therefore we may take tangent on both sides, and the solution set will remain the same.

This gives  `2x - 5 = tan(-1) = -tan(1),` so the only solution is `x = (5 - tan(1))/2 approx 1.72.`

The range of arctan function is `(-pi/2, pi/2),` on which interval tangent function is strictly monotone. Therefore we may take tangent on both sides, and the solution set will remain the same.

This gives  `2x - 5 = tan(-1) = -tan(1),` so the only solution is `x = (5 - tan(1))/2 approx 1.72.`