Evaluate each expression for p=-4, q=8, and r=-10. 5r / 2p-3r

Verified step by step guidance

1. First, substitute the given values into the expression. The expression is \(\frac{5r}{2p - 3r}\), and the values are \(p = -4\), \(q = 8\), and \(r = -10\). Since \(q\) is not in the expression, focus on \(p\) and \(r\).
2. Replace \(r\) with \(-10\) and \(p\) with \(-4\) in the expression: \(\frac{5(-10)}{2(-4) - 3(-10)}\).
3. Simplify the numerator by multiplying: \(5 \times (-10) = -50\), so the numerator becomes \(-50\).
4. Simplify the denominator by performing the multiplications first: \(2 \times (-4) = -8\) and \(3 \times (-10) = -30\). Then substitute these back into the denominator: \(-8 - (-30)\).
5. Simplify the denominator by subtracting a negative number, which is equivalent to addition: \(-8 + 30\). Then, write the simplified expression as \(\frac{-50}{22}\).

Key Concepts

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This is essential for evaluating expressions when specific values for variables are provided, allowing the expression to be simplified to a numerical result.

Order of Operations

The order of operations dictates the sequence in which parts of a mathematical expression are evaluated, typically following PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Correct application ensures accurate simplification of expressions.

Simplifying Algebraic Expressions

Simplifying involves performing arithmetic operations and combining like terms to reduce an expression to its simplest form. This includes handling multiplication, division, and subtraction correctly after substitution to find the final value.