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The given equation is 鈥�$7x+5\left(x鈭�1\right)=鈭�5+12x$鈥�.

Solving,

$7x+5\left(x鈭�1\right)=鈭�5+12x$ (Given equation)

$7x+5x鈭�5=鈭�5+12x$ (Distributive property)

$12x鈭�5=鈭�5+12x$ (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 $x$.

Put $x=1$in the given equation $7x+5\left(x鈭�1\right)=鈭�5+12x$to get,

$\begin{array}{l}7+5\left(1鈭�1\right)=鈭�5+12\\ 7+5\left(0\right)=7\\ 7+0=7\\ 7=7\end{array}$

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

Put $x=0$in the given equation $7x+5\left(x鈭�1\right)=鈭�5+12x$to get,

$\begin{array}{l}7\left(0\right)+5\left(0鈭�1\right)=鈭�5+12\left(0\right)\\ 0+5\left(鈭�1\right)=鈭�5+0\\ 鈭�5=鈭�5\end{array}$

Since the values on the left-hand side and the right-hand side are equal, it can be said that $x=0$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.