Solve each equation. Check your solution.

$5h-7=5\left(h-2\right)+3$

The given equation is “$5h-7=5\left(h-2\right)+3$”.

Solving,

$5h-7=5\left(h-2\right)+3$ (Given equation)

$5h-7=5h-10+3$ (Distributive property)

$5h-7=5h-7$ (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 h.

Put $h=1$in the given equation $5h-7=5\left(h-2\right)+3$to get,

$\begin{array}{l}5-7=5\left(1-2\right)+3\\ -2=5\left(-1\right)+3\\ -2=-5+3\\ -2=-2\end{array}$

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

Put $h=0$in the given equation $5h-7=5\left(h-2\right)+3$to get,

$\begin{array}{l}5\left(0\right)-7=5\left(0-2\right)+3\\ 0-7=5\left(-2\right)+3\\ -7=-10+3\\ -7=-7\end{array}$

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