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Solving equations is a fundamental skill in algebra. When you solve an equation, you are finding the value of the variable that makes the equation true. The main goal is to isolate the variable on one side of the equation. To do this, you usually perform a series of algebraic manipulations that simplify the equation step by step.

In the example given, the task is to solve the equation \(-6x + 4 = -8\). We start by simplifying the equation in such a way that we get close to having just the variable on one side. This often involves

• adding or subtracting terms from both sides
• multiplying or dividing both sides by a number

Once the equation is simplified, it's straightforward to find the solution. Though these operations may seem arbitrary, they are based on the principle that we want to maintain equality by performing the same operation on both sides of the equation.

Linear equations are a specific type of algebraic equation where the highest power of the variable is 1. They typically appear in the form \( ax + b = c \), where \( a \), \( b \), and \( c \) are constants.

In our example, the equation \(-6x + 4 = -8\) is a linear equation because the variable \( x \) is not raised to any power other than 1. Solving linear equations like this often involves

• balancing terms on either side of the equation
• simplifying expressions by combining like terms

The simplicity of linear equations makes them the building blocks for understanding more complex algebraic expressions and equations. Once you are familiar with the process, you can apply similar techniques to solve more complicated algebraic structures.

Using a step-by-step solution process can help clarify how to solve an equation by methodically breaking down the steps involved.

Simplification Step

The first crucial step is to simplify the equation. We begin with the equation \(-6x + 4 = -8\). By subtracting 4 from both sides, we balance the equation and make it simpler: \(-6x = -12\). This allows us a clearer path towards isolating the variable.

Solving for the Variable

With the equation now simplified to \(-6x = -12\), we aim to solve for \( x \). The variable \( x \) has a coefficient of \(-6\), which can be removed by dividing each term by \(-6\). This gives \( x = 2 \), which is the solution. Each of these steps demonstrates a logical and precise method that keeps the equation balanced, leading directly to the solution.