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Solving equations involves finding the value of an unknown variable that makes the equation true. In the equation \(15x - 2 = 43\), \(x\) is our unknown variable. To solve such equations, we perform a series of steps that maintain the equality while gradually isolating the variable.When you solve an equation, remember that any operation you perform on one side of the equation must also be performed on the other side. This maintains the balance of the equation, ensuring that it remains true. Think of it as maintaining fairness in mathematics, where what you do to one side, you must do to the other.The goal is always to manipulate the equation such that the variable of interest is isolated on one side of the equation. This principle forms the foundation of solving linear equations.

Isolating variables is the process of rearranging an equation so that the variable you want to solve for stands alone on one side. In our example, \(15x - 2 = 43\), the first step to isolating \(x\) is to deal with the \(-2\), which is attached to our variable term.

• First, eliminate the constant term by adding 2 to both sides of the equation.
• This action results in \(15x = 45\).

Now the variable term is simplified to \(15x\). The process of isolating the variable involves simplifying each side as much as possible until the variable is by itself, making it easier to identify its value.Isolating variables is crucial because it helps to clearly see the solution of the equation. By focusing on removing other terms around the variable, you eliminate the 'noise' and focus purely on finding the solution.

Mathematical operations such as addition, subtraction, multiplication, and division are the tools we use to manipulate equations. Each operation plays a critical role in the process of solving equations.In our original equation \(15x - 2 = 43\), we initially used addition:

• Adding 2 eliminated the subtraction of 2, simplifying the equation to \(15x = 45\).

Next, we used division:

• To completely isolate \(x\), we divided both sides by 15. This gives us \(x = 3\), completing the solution.

These operations help us to systematically dismantle equations into simpler components, leading us step-by-step to the solution. Understanding which operation to use at each step is key to solving for the variable efficiently and accurately.