Solve the equation for $\mathrm{x}$, where $\mathrm{x}$ is restricted to the given interval.
\[
y=\tan x-6, \text { for } x \text { in }\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
\]
\[
x=
\]

Step 1 ：The equation is given as \(y = \tan(x) - 6\), where \(x\) is restricted to the interval \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\).

Step 2 ：To solve for \(x\), we need to isolate \(x\) on one side of the equation. This can be done by adding 6 to both sides of the equation to get \(y + 6 = \tan(x)\).

Step 3 ：We can then use the inverse tangent function, also known as arctan or \(\tan^{-1}\), to solve for \(x\). The inverse tangent function undoes the tangent function, so \(x = \arctan(y + 6)\).

Step 4 ：However, we need to keep in mind that the \(\arctan\) function returns a value in the interval \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), which is the same interval given in the question.

Step 5 ：\(\boxed{x = \arctan(y + 6)}\) for \(x\) in \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\) is the final solution to the equation.