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Theory

When rewriting equations it's important to make the the same operation on both sides to ensure that the equality still holds. So, if a number is added to one side, the same number must be added to the other side. In the equation $4x-7=5,$ $7$ can be added to both sides. $4x-7{\color{#FF0000}{\,+\,7}}=5{\color{#FF0000}{\,+\,7}} \quad \Leftrightarrow \quad 4x = 12$