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Understanding algebra is essential as it forms the foundation for solving equations. Algebra often involves using symbols like \(x\) to represent unknown values. These symbols are used to create equations. An equation is a mathematical statement indicating that two expressions are equal. In algebra, we try to find the value of these unknowns by solving the equations. For instance, in the equation \(-3x - 6 = 12\), \(x\) is the unknown variable we want to solve for.

To work with algebra, it’s vital to understand and apply the order of operations and perform operations such as addition, subtraction, multiplication, and division to manipulate the equations. By strategically performing these operations, the equation is simplified, and the value of the variable can be determined. Remember, whatever operation you perform on one side of the equation must be performed on the other side to maintain balance.

The process of solving equations involves a systematic approach to isolate the variable on one side of the equation. Let’s break down the technique using the example \(-3x - 6 = 12\).

**Step 1: Eliminate Constants**

• First, remove or cancel out any constants present with the variable by performing inverse operations. In this example, add 6 to both sides, turning the equation into \(-3x = 18\).

**Step 2: Isolate the Variable**

• Next, you need to isolate the variable \(x\) by dividing both sides by \(-3\). This step gives you \(x = -6\). By dividing, you are getting \(x\) alone on one side of the equation.

Remember, each step should bring you closer to expressing the variable alone on one side of the equation. Keeping the equation balanced throughout this process is crucial.

Once you find the potential solution to an equation, always verify it to ensure accuracy. Checking your solution helps confirm that you've done all the steps correctly. Let’s verify the solution for \(x = -6\) in our equation \(-3x - 6 = 12\).

**Substitution:**

• Replace \(x\) with \(-6\) in the original equation: \(-3(-6) - 6 = 12\).

**Simplification:**

• Simplify the left side: compute \(-3 \times -6 = 18\), then \(18 - 6 = 12\), which matches the right side.

This tells us that \(x = -6\) is indeed the correct solution. Checking solutions not only helps in confirming correctness but also in understanding the consistency of algebraic principles. It is a crucial final step when solving any algebra equation.