91Ó°ÊÓ

In algebra, variables act as placeholders for numbers we do not know yet. When an exercise provides specific values for these variables, the next step is to replace the variables with these numbers. This is known as variable substitution. Think of it as swapping or replacing the letter in your expression with a specific number value.
For example, if you're given an expression like \(y - z\), and it's stated that \(y = 8\) and \(z = -12\), substitute each variable with the number it represents:

• Replace \(y\) with \(8\).
• Replace \(z\) with \(-12\).

This substitution transforms the original algebraic expression into one that only contains numbers: \(8 - (-12)\). Remember, this is a crucial first step in making complex algebraic expressions more manageable.

When evaluating an expression that has more than one operation, it's essential to follow the order of operations to arrive at the correct answer. This is often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In the equation \(8 - (-12)\), we see the operation of subtraction. However, due to the presence of a negative sign, it gets a bit tricky. When we have subtraction like this \(8 - (-12)\), we have to first acknowledge that subtracting a negative is the same as adding the opposite. This means:

• Subtracting a negative number converts it into a positive addition.
• Thus, \(8 - (-12)\) becomes \(8 + 12\).

Following the order of operations correctly ensures you calculate the expression properly and avoid common mistakes.

Simplifying an expression involves combining like terms and performing all possible operations to reduce it to its simplest form. Once you've done the variable substitution and followed the order of operations, the next step is simplification. In our exercise, after substituting and transforming \(8 - (-12)\) into \(8 + 12\), we simplify by actually performing the addition:

• Add \(8 + 12\).
• The result is \(20\).

This straightforward calculation shows the power of simplification: it takes a potentially confusing expression (especially involving negatives) and reduces it to something clear and understandable. This step confirms your understanding that canceling double negatives results in a simple addition.