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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. R - Algebra ReviewProblem R.2.103
Chapter 1, Problem R.2.103

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

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First, substitute the given values of \( p = -4 \), \( q = 8 \), and \( r = -10 \) into the expression: \( - (p + 2)^2 - 3r \) divided by \( 2 - q \).
Rewrite the expression with the substituted values: \( - (-4 + 2)^2 - 3(-10) \) over \( 2 - 8 \).
Calculate the value inside the parentheses in the numerator: \( (-4 + 2) = -2 \), then square it to get \( (-2)^2 \).
Evaluate the numerator by applying the negative sign outside the square, then subtract \( 3r \) (remember \( r = -10 \)), so compute \( - (-2)^2 - 3(-10) \).
Calculate the denominator by subtracting \( q \) from 2: \( 2 - 8 \), then divide the evaluated numerator by this denominator to complete the expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses first, then exponents, followed by multiplication and division (left to right), and finally addition and subtraction (left to right). This ensures consistent and correct evaluation of expressions.
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Substitution of Variables

Substitution involves replacing variables in an expression with their given numerical values. This step is essential to evaluate expressions numerically, allowing the transformation of an algebraic expression into a specific number.
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Evaluating Exponents and Negative Signs

When evaluating expressions with exponents, it is important to correctly apply powers to quantities, especially when negative signs and parentheses are involved. For example, squaring a negative number inside parentheses affects the sign of the result, while a negative sign outside the parentheses changes the overall sign after exponentiation.
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