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

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Identify the given expression to evaluate: \(3p - 2r\).

Substitute the given values into the expression: replace \(p\) with \(-4\) and \(r\) with \(-10\), so the expression becomes \(3(-4) - 2(-10)\).

Apply the multiplication operations: calculate \(3 \times (-4)\) and \(-2 \times (-10)\) separately.

Simplify the expression by performing the multiplications and then combine the results using subtraction.

Write the simplified expression as the final evaluated result (without calculating the numeric value here).

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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.

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Equations with Two Variables

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.

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Algebraic Operations on Vectors

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.

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