There are many ways to write equivalent expressions, and they may look very different from each other. One way to determine if two expressions are equivalent or not is to substitute the same number for the variable in both expressions.

For example, when $x$ is 1, the expression $2(\text-3+x)+8$ equals 4 and the expression $2x+5$ equals 7. This means $2(\text-3+x)+8$ and $2x+5$ are not equivalent.

If two expressions are equal when many different values are substituted for the variable, then the expressions may be equivalent—it is impossible to compare the two expressions for all values. To know for sure, we use properties of operations. For example, $2(\text-3+x)+8$ is equivalent to $2x+2$ because:

$\begin{aligned} 2(\text-3+x)+8\\ \text-6+2x+8 & \quad\text{by the distributive property}\\ 2x+\text-6+8 & \quad\text{by the commutative property}\\ 2x+(\text-6+8) & \quad\text{by the associative property} \\ 2x+2 \\ \end{aligned}$