Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6.3p - 2r

Verified step by step guidance

1. Substitute the given values into the expression: replace \( p \) with \( -4 \) and \( r \) with \( -10 \).
2. The expression becomes \( 3(-4) - 2(-10) \).
3. Calculate \( 3(-4) \) which involves multiplying 3 by -4.
4. Calculate \( -2(-10) \) which involves multiplying -2 by -10.
5. Combine the results of the two calculations to simplify the expression.

Key Concepts

Substitution

Substitution is the process of replacing variables in an expression with their corresponding values. In this case, we substitute p, q, and r with -4, 8, and -10, respectively. This allows us to evaluate the expression accurately by simplifying it to a numerical value.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions, following this order is crucial to obtaining the correct answer.

Linear Expressions

Linear expressions are algebraic expressions that involve constants and variables raised to the first power. The expression 3p - 2r is linear because it consists of terms that are linear combinations of the variables p and r. Understanding linear expressions is essential for simplifying and evaluating them correctly.