91Ó°ÊÓ

In mathematics, variables are symbols that represent unknown values. When you have an expression like \( x-y+z \), each letter represents a placeholder for a number. Variable substitution is the process of replacing these symbols with actual numbers.

In our example, the problem gives specific values: \( x = 5 \), \( y = 6 \), and \( z = -9 \). We substitute these values into the expression. This means we replace \( x \) with \( 5 \), \( y \) with \( 6 \), and \( z \) with \( -9 \).

The aim of substitution is to transform the algebraic expression into an arithmetic one, using known values to solve the problem. This is a crucial step as it converts theoretical problems into practical calculations.

Arithmetic operations are the foundation of mathematics, comprising addition, subtraction, multiplication, and division. In algebra, once variables are substituted with numbers, these operations help us solve the expressions.

For the expression \( x-y+z \) which becomes \( 5 - 6 + (-9) \) after substitution, we need to apply arithmetic operations sequentially.

• The first operation is subtraction: calculate \( 5 - 6 \), which equals \(-1\).
• Then, proceed to the next operation: add \(-9\), leading to the expression \(-1 - 9\).

By performing these operations step by step, the expression is simplified, arriving at a final numerical result.

Negative numbers are numbers less than zero, indicated by a minus sign \((-)\). When dealing with expressions, understanding how to handle negative numbers is essential.

In the expression \( x - y + z \) converted to \( 5 - 6 - 9 \), notice that \( z \) is \(-9\).

• Subtracting a number is equivalent to adding its negative, meaning \( -9 = + (-9) \).
• When subtracting a positive number - like \( 6 \) in the equation - it reduces the total value.
• When negative numbers are involved, each operation affects the outcome significantly. For instance, subtracting \(-9\) from \(-1\) leads to more decrement, arriving at \(-10\).

Grasping how negative numbers interact in arithmetic operations is crucial for correctly evaluating expressions.