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Solving equations is a foundational skill in algebra. The goal is to find the unknown variable that makes the equation true. In our example, we start with the equation: \(2x = -5\). To solve this, we need to determine the value of \(x\) that makes both sides of the equation equal.

This process often involves using different algebraic techniques such as addition, subtraction, multiplication, or division to isolate the variable. Following these steps carefully ensures we find the correct solution.

Isolating the variable is a crucial step in solving equations. In our equation, \(2x = -5\), we need to get \(x\) alone on one side of the equation. Here’s how to do it:

- Identify the coefficient of \(x\), which is the number multiplying \(x\). In this case, it's 2.
- Use the multiplication principle, which says you can divide or multiply both sides of the equation by the same non-zero number without changing the equation’s equality.
- Divide both sides by 2:
\[ \frac{2x}{2} = \frac{-5}{2} \]
- This operation simplifies the left side to \(x\) and the right side to \(-\frac{5}{2}\). As a result, we find \(x = -\frac{5}{2}\).

By isolating the variable, we have determined that \(x\) is equal to \(-2.5\).

After finding a solution, it’s important to check it to ensure it’s correct. We do this by substituting the value of the variable back into the original equation. Here’s how to check:

- Original equation: \(2x = -5\).
- Our solution is \(x = -2.5\).
- Substitute \(x = -2.5\) into the equation:
\[ 2(-2.5) = -5 \]
- Performing the calculation:
\(-5 = -5 \).
Since both sides of the equation are equal, the solution is validated.

This step is crucial as it confirms that the value we calculated is indeed the correct solution for the given equation. It’s always good practice to check your solutions in algebra.