91Ó°ÊÓ

Solving equations, especially linear ones, is about finding the value of an unknown variable that makes the equation true. In the given exercise, our equation is \( 2x = 12 \). This is a linear equation because it is of the form \( ax = b \), where \( a \) and \( b \) are constants. To solve such an equation, our goal is to determine the value of \( x \) that satisfies the equation.

When solving equations, it's important to maintain balance. Think of an equation as a balanced scale: whatever you do to one side, you must also do to the other. The key steps often involve performing inverse operations to simplify the equation and find the solution. In this exercise, the operation involved is multiplication, and we will use division to cancel it out.

Isolating the variable is a crucial step in solving equations. The objective is to get the variable you are solving for, in this case, \( x \), by itself on one side of the equation. In our equation, \( 2x = 12 \), \( x \) is currently multiplied by 2. To isolate \( x \), perform the inverse of multiplication, which is division.

Here's how it works:

• Divide both sides of the equation by 2, which is the coefficient of \( x \).
• This operation gives us \( x = \frac{12}{2} \).

By dividing both sides by 2, you effectively cancel out the 2 that \( x \) is multiplied by, allowing \( x \) to stand alone. Isolating variables helps to see clearly what the value of the variable is once the equation is simplified.

Simplifying expressions is the process of making a mathematical expression easier to understand and solve. After isolating the variable \( x \) and setting up \( x = \frac{12}{2} \), we then simplify the expression.

This involves performing the arithmetic operation: dividing 12 by 2. Simplification helps to reduce the expression into its simplest form:

• Calculate \( \frac{12}{2} \).
• The result is 6.
• Therefore, \( x = 6 \).

Simplifying expressions not only aids in solving the equation but also ensures clarity and precision. It is the final step that confirms the solution you obtained is correct and presented in the simplest terms.