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Evaluating an expression is like finding the answer to a mathematical statement. In our exercise, we're given variables \(x = 10\), \(y = -4\), and \(z = -15\) to evaluate the expression \(y - x\). First, understand that expression evaluation involves substituting these variable values into the expression.

Let's say we need to substitute \(y = -4\) and \(x = 10\) into the expression \(y - x\). This substitution is a straightforward process. Wherever you see a \(y\), replace it with \(-4\), and wherever you see an \(x\), replace it with \(10\).

After substitution, the expression becomes \(-4 - 10\). This process of substitution is crucial because it translates the given algebraic expression into a numerical one that can be solved through arithmetic operations.

Working with integers is fundamental in mathematics. Integers include all whole numbers and their negatives. In our exercise, we handle integer operations by simplifying \(-4 - 10\). This leads us to performing subtraction operations with integers.

Subtraction of integers can be viewed as adding the opposite. Instead of thinking of it as \(-4 - 10\), consider it as \(-4 + (-10)\). This translation helps clarify that you're adding two negative numbers.

• When subtracting a positive integer, envision adding its negative.
• When subtracting a negative integer, you will add its positive counterpart.

Understanding this helps simplify integer operations and avoid confusion with subtraction and addition.

Navigating negative numbers can sometimes feel challenging, but it's simpler if you follow a consistent approach. In our example, we evaluated \(-4 + (-10)\). Handling negative numbers often just means staying aware of their direction on the number line.

When you add two negative numbers like \(-4\) and \(-10\), you're essentially moving further left on the number line. It’s like combining their absolute values and adding a negative sign, resulting in \(-14\).

• Adding two negative numbers increases their absolute value but keeps the overall number negative.
• If you were subtracting a negative number, it would be similar to adding a positive number.

Remember, the luck of understanding negative numbers is recognizing their position on the number line. Use this as a guide to predict results effectively.