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The given equation is 鈥�$鈭�5\left(3鈭�q\right)+4=5q鈭�11$鈥�.

Solving,

$鈭�5\left(3鈭�q\right)+4=5q鈭�11$ (Given equation)

$鈭�15+5q+4=5q鈭�11$ (Distributive property)

$5q鈭�11=5q鈭�11$ (Simplify)

The expressions on both sides are identical.

This implies that the given equation is an identity. So, it is true for all values of $q$.

Put $q=1$in the given equation $鈭�5\left(3鈭�q\right)+4=5q鈭�11$to get,

$\begin{array}{l}鈭�5\left(3鈭�1\right)+4=5鈭�11\\ 鈭�5\left(2\right)+4=鈭�6\\ 鈭�10+4=鈭�6\\ 鈭�6=鈭�6\end{array}$

Since the values on the left-hand side and the right-hand side are equal, it can be said that $q=1$is a solution of the given equation.

Put $q=0$in the given equation $鈭�5\left(3鈭�q\right)+4=5q鈭�11$to get,

$\begin{array}{l}鈭�5\left(3鈭�0\right)+4=5\left(0\right)鈭�11\\ 鈭�5\left(3\right)+4=0鈭�11\\ 鈭�15+4=鈭�11\\ 鈭�11=鈭�11\end{array}$

Since the values on the left-hand side and the right-hand side are equal, it can be said that $q=0$is a solution of the given equation.

Thus, it can be seen that a linear equation has at least two different solutions. This verifies that the given equation is an identity.