Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 3p - 2r

Verified step by step guidance

1. Identify the given expression to evaluate: \$3p - 2r$.
2. Substitute the given values into the expression: replace \(p\) with \(-4\) and \(r\) with \(-10\), so the expression becomes \$3(-4) - 2(-10)$.
3. Apply the multiplication operations: calculate \(3 \times (-4)\) and \(-2 \times (-10)\) separately.
4. Simplify the expression by performing the multiplications and then combine the results using subtraction.
5. Write the simplified expression as the final evaluated result (without calculating the numeric value here).

Key Concepts

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This is essential for evaluating expressions like 3p - 2r by directly inserting the values of p and r to simplify and find the result.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed, typically parentheses, exponents, multiplication/division, and addition/subtraction. Correctly applying this ensures accurate evaluation of expressions such as 3p - 2r.

Multiplication of Integers

Multiplying integers, including negative numbers, follows specific rules: the product of two negatives is positive, and the product of a positive and a negative is negative. Understanding this is crucial when calculating terms like 3p and 2r with negative values.