Evaluate each expression for x = -4 and y = 2. 2|y| - 3|x| / |xy|

Verified step by step guidance

1. First, substitute the given values into the expression: replace \( x \) with \( -4 \) and \( y \) with \( 2 \) in the expression \( 2|y| - \frac{3|x|}{|xy|} \).
2. Calculate the absolute values: find \( |y| \), \( |x| \), and \( |xy| \). Remember that the absolute value of a number is its distance from zero, so it is always non-negative.
3. Rewrite the expression with the absolute values calculated: \( 2|y| - \frac{3|x|}{|xy|} \) becomes \( 2 \times |2| - \frac{3 \times | -4 |}{|(-4)(2)|} \).
4. Perform the multiplications and division inside the expression step-by-step: multiply \( 2 \times |2| \), multiply \( 3 \times | -4 | \), and then divide by \( |(-4)(2)| \).
5. Finally, subtract the fraction from the product \( 2|y| \) to get the simplified expression value.

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. For example, |x| equals x if x is positive or zero, and -x if x is negative. This concept is essential for correctly evaluating expressions involving absolute values.

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. Here, x and y are replaced with -4 and 2 respectively, allowing the expression to be evaluated numerically. Accurate substitution is crucial for solving algebraic expressions.

Order of Operations

The order of operations dictates the sequence in which parts of an expression are evaluated, typically parentheses, exponents, multiplication/division, and addition/subtraction (PEMDAS). Applying this correctly ensures the expression is simplified accurately, especially when fractions and absolute values are involved.