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

Verified step by step guidance

1. Step 1: Identify the given values for the variables: \( p = -4 \), \( q = 8 \), and \( r = -10 \).
2. Step 2: Substitute the given values into the first expression \( q + r \).
3. Step 3: Perform the addition for the expression \( q + r \) by adding \( q = 8 \) and \( r = -10 \).
4. Step 4: Substitute the given values into the second expression \( q + p \).
5. Step 5: Perform the addition for the expression \( q + p \) by adding \( q = 8 \) and \( p = -4 \).

Key Concepts

Substitution in Algebra

Substitution is a fundamental algebraic technique where specific values are replaced in an expression or equation. In this case, the variables p, q, and r are substituted with their respective values (-4, 8, and -10) to evaluate the expressions. This process simplifies the expressions, allowing for straightforward calculations.

Addition of Integers

Addition of integers involves combining whole numbers, which can be positive or negative. When adding integers, the sign of the numbers affects the result; for example, adding a positive number to a negative number requires determining which number has a greater absolute value. Understanding how to handle positive and negative integers is crucial for accurately evaluating the expressions.

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 when evaluating expressions to avoid errors in calculations, especially when multiple operations are involved.