2. Solve 2 tan x + 6 = -tan x + 3 on [0, 2(pie))
Your answer

If I understand your question correctly I would say X= 3pi/4.

In which people move all of the terms containing tan X to the left side of the equation.

You’ll get, 3tan(X) + 6 = 3

Move all of the terms not containing tan (X) to the right side of the equation.

3tan (X) = -3

Then divide each term by three and simplified.

Tan (X) = -1

Take the inverse tangent of both sides of the equation to extract X from inside the tangent.

X = arctangent (-1)

The exact value of arctangent (-1) is
- pi/4.

The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from pi to find the solution in the third quadrant.

X = - pi/4 - pi

Simplify the expression to find the second solution.

X = 3pi/4

I hope that helps.