Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 5r———2p - 3r

Verified step by step guidance

1. Substitute the given values into the expression: \( \frac{5r}{2p - 3r} \) becomes \( \frac{5(-10)}{2(-4) - 3(-10)} \).
2. Calculate the numerator: \( 5(-10) = -50 \).
3. Calculate the first part of the denominator: \( 2(-4) = -8 \).
4. Calculate the second part of the denominator: \( 3(-10) = -30 \).
5. Combine the results in the denominator: \( -8 - (-30) = -8 + 30 \).

Key Concepts

Substitution

Substitution is the process of replacing variables in an expression with their corresponding numerical values. In this question, we substitute p, q, and r with -4, 8, and -10, respectively. This step is crucial for evaluating the expression accurately, as it transforms the algebraic expression into a numerical one that can be simplified.

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. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this concept is essential for evaluating expressions correctly, especially when multiple operations are involved.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form by performing operations and combining like terms. In this case, after substituting the values for p, q, and r, we will simplify the expression by carrying out the arithmetic operations in the correct order, leading to a final numerical result that answers the question.