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Isolating the variable, often represented by letters such as x or y, is a critical step in solving linear equations. The goal is to have the unknown variable on one side of the equation and the constants or numbers on the other. This process transforms the equation and makes the value of the variable clear.

To isolate the variable in the equation x + 7 = -14, we need to eliminate all other terms that are currently on the same side as x. This is typically done using inverse operations, such as subtraction if a number is added to the variable, or addition if a number is subtracted. In this case, since 7 is added to x, we need to subtract 7 to get the variable x by itself.

Subtracting from both sides is a strategy used when you're trying to maintain the balance of an equation while isolating a variable. Think of a scale in equilibrium – whatever you do to one side, you must do to the other to keep it balanced.

For our equation x + 7 = -14, subtract 7 from both sides to maintain balance. This step is shown as:
\[ x + 7 - 7 = -14 - 7 \] Following the principle of equality, if you remove 7 hostages from each side of the equation, you keep the scales of justice even. Hence, on the left side, 7 - 7 cancels out, leaving x by itself. On the right side, you're left with -14 - 7. This is a straightforward arithmetic calculation that simplifies to find the value of x.

The solution of an equation is the value of the variable that makes the equation true. This value is sometimes referred to as the 'root' of the equation. In other words, if you substitute this value back into the original equation, both sides should equal the same amount verifying the correctness of the solution.

After subtracting 7 from both sides in the problem x + 7 = -14, we simplified the equation to x = -21. To verify this, if we place -21 back into the original equation in place of x, it should look like this:
\[ (-21) + 7 = -14 \] When we calculate the left side, -21 + 7, it indeed equals -14, which confirms that our solution, x = -21, is correct. Understanding how to solve for solutions means you not only know how to find them but also how to check your work for accuracy.