91Ó°ÊÓ

When solving linear equations, our goal is to find the value of the variable that makes the equation true. A linear equation is one where the highest power of the variable is one, like the example: \(5x - 2 = 18\). Here, "\(x\)" is our variable. To solve these equations, we often perform operations to both sides to simplify and isolate the variable.

The steps usually include picking out constants from the equation and performing the opposite arithmetic operation on both sides to simplify. Adding, subtracting, multiplying, or dividing every term equally maintains the balance of the equation, ensuring that it remains true.

• Addition or subtraction to remove constants or adjust terms
• Multiplication or division to simplify and solve for the variable

By using these steps, we can systematically solve linear equations in a clear and logical manner.

Isolating the variable means rearranging the equation so that the variable stands alone on one side of the equation sign. In our specific problem \(5x - 2 = 18\), the first step is to get rid of the constant \(-2\) next to \(5x\). This is done by adding 2 to both sides, allowing us to focus on the term with \(x\).

After the addition, we are left with \(5x = 20\), moving one step closer to finding \(x\). The goal is to have the variable \(x\) by itself on one side, which we achieve by modifying the equation accordingly. Once the variable is on its own, it's straightforward to determine its value.

A step-by-step solution breaks the problem down into smaller, more manageable actions, making it easier to follow and understand. Here's how we can apply this approach to our equation:

• Step 1: Identify the constant to move. We began by adding \(2\) to both sides:
  \(5x - 2 + 2 = 18 + 2\) simplifies to \(5x = 20\).
• Step 2: Solve for the variable \(x\). Here, divide both sides by \(5\):
  \(x = \frac{20}{5}\), which simplifies to \(x = 4\).

By tackling each part of the equation methodically, it guides us to a correct solution. Step-by-step solutions are pivotal for understanding how each component of the equation is handled, ensuring the procedure remains clear and logical throughout.