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Algebra is a branch of mathematics that deals with numbers and letters (variables). It's like solving puzzles where you find the value of the unknowns. In our problem, the equation is given as \(-4 = 2x - 6\). The goal is to figure out the value of the variable \(x\), which is the unknown.

Algebraic equations consist of expressions on each side of an equality sign (\(=\)). These expressions can have numbers, variables, and mathematical operators like addition, subtraction, multiplication, and division.

• Variables in algebra represent unknown numbers.
• By manipulating these equations, we discover the values of these unknowns.

Algebra is essential because it provides a means of expressing complicated relationships in a manageable form.

Let's delve deeper into the techniques used to isolate the variable.

Isolating the variable is a critical step in solving algebraic equations. The idea is to 'uncover' the variable by itself on one side of the equation to find its value. For our equation \(-4 = 2x - 6\), the main task is to get \(x\) alone on one side.

Here’s how we achieve this:
1. **Move the Constant Term**: Begin by adding or subtracting terms to both sides to move constants away from the side containing the variable. In our case, adding 6 to both sides removes \(-6\) from the side with \(x\).

\(-4 + 6 = 2x - 6 + 6\)

2. **Simplify the Equation**: After moving terms, simplify by performing the arithmetic operations. The equation \(-4 + 6 = 2x\) simplifies to \(2 = 2x\). Now, the equation looks neater and focuses more on the variable.

Isolating the variable makes solving the equation much easier. Let's see how this leads us to the solution.

Once the variable is isolated with terms only involving the variable on one side, we proceed to solve the equation to find its value. Follow these steps to continue:

1. **Divide or Multiply to Solve**: To find \(x\), you need to eliminate the coefficient attached to it. Coefficients are the numbers that multiply the variable. In \(2 = 2x\), the coefficient is 2.

• Divide both sides by 2 to keep the equation balanced: \(\frac{2}{2} = \frac{2x}{2}\)

2. **Simplify the Final Result**: Performing arithmetic, you simplify to find \(x = 1\). Congratulations! You've solved for \(x\).

This approach of handling equations, by carefully making moves like balancing a scale, is fundamental in algebra. Solving equations step by step ensures that each move made maintains the balance of the equation, leading to accurate results.