91Ó°ÊÓ

Linear equations are fundamental in algebra and involve finding unknown values that satisfy the equation. A linear equation is one in which the highest exponent of the variable is 1. These equations generally have a straightforward solution process.
When solving linear equations like \( n - 0.5n = 12 \), our goal is to find the value of \( n \) that makes the equation true. Start by simplifying each side of the equation if possible, and then use inverse operations to isolate the variable on one side of the equation.
For example, in the given equation, we simplify first to combine like terms and then solve for \( n \) by dividing. These steps ensure we systematically reduce the complexity of the problem, ultimately finding the precise numerical value of the unknown.

Simplifying an expression is a crucial step in solving algebraic equations. It involves breaking down expressions into their simplest form, making them easier to handle.
Consider the expression \( n - 0.5n \). Here, we recognize that both \( n \) and \( 0.5n \) are like terms because they include the variable \( n \). We aim to combine these terms to simplify the expression.
In this case, \( n \) is equivalent to \( 1n \), so the expression \( n - 0.5n \) can be rewritten as \( 1n - 0.5n \), which simplifies to \( 0.5n \). This simplification reduces the original expression to a much simpler one that we can solve more easily.

Combining like terms is a fundamental algebraic technique used to simplify expressions and solve equations.
Like terms are terms whose variables and their exponents are identical. In the equation \( n - 0.5n = 12 \), both \( n \) (treated as \( 1n \)) and \( -0.5n \) are like terms because the variable \( n \) is the same in both.

• Group terms with similar variables and exponents.
• Add or subtract the coefficients of the similar terms.

By subtracting \( 0.5n \) from \( 1n \), we find our simplified expression, \( 0.5n \).
This enables us to isolate the variable more easily and continue solving the equation. Combining like terms reduces the complexity of algebraic expressions and is a necessary step in the simplification process. By understanding and applying this technique, you set a strong foundation for solving more complex equations.