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When tackling linear equations like \(4x - 6 = 18\), the goal is to find the value of \(x\) that makes the equation true. Linear equations contain variables (like \(x\)) and constants. To solve them, focus on isolating the variable on one side of the equation. Generally, you simplify one side at a time using basic operations like addition, subtraction, multiplication, or division.

Remember that what you do to one side of the equation, you must do to the other. This maintains balance. In our exercise, we solve the equation by reversing the operations applied to \(x\):

• Addition/Subtraction: Move constants to the opposite side to simplify.
• Multiplication/Division: Isolate \(x\) by removing coefficients.

By following these steps, we maintain a balanced equation, allowing us to solve for the unknown variable effectively.

Understanding each step in solving an equation helps you grasp the process more clearly. Let's break down the solution for the equation \(4x - 6 = 18\):

Step 1: Add 6 to Both Sides
We start by eliminating the \(-6\) from the left side. Adding 6 to both sides results in \(4x - 6 + 6 = 18 + 6\). This simplifies our equation to \(4x = 24\). By adding 6, we counteract the negative sign and simplify the variable-side.Step 2: Divide by 4
Next, remove the coefficient of \(x\), which is 4, by dividing each side of the equation by 4: \(\frac{4x}{4} = \frac{24}{4}\). This gives us \(x = 6\). Dividing both sides ensures the equation remains balanced. Each of these steps is crucial to isolating \(x\) and finding its value.

Grasping basic algebra concepts lays the foundation for solving equations seamlessly. Here are a few key ideas relevant to our exercise:

• Variables: Symbols like \(x\) represent unknown numbers. Solving equations means figuring out what value fits the variable.
• Constants: Regular numbers, like 6 and 18 in our equation, are fixed values that modify the variable term.
• Coefficients: Numbers multiplying the variable, such as 4 in \(4x\), which indicate how many times the variable is added to itself.
• Maintaining Equation Balance: Any operation you perform on one side of the equation must be mirrored on the other to keep it balanced and equal.
• Goal of Solving: The ultimate aim is to solve for the variable, providing a value that satisfies the equation. This means the equation makes sense when the variable is replaced by the solved value (like \(x = 6\)).

Understanding these concepts allows you to apply strategies efficiently to solve more complex equations as you progress in algebra.