Evaluate each expression for x = -4 and y = 2. |-8y + x| / -|x|

Verified step by step guidance

1. First, substitute the given values of \( x = -4 \) and \( y = 2 \) into the expression \( \frac{| -8y + x |}{- |x|} \).
2. Calculate the expression inside the absolute value in the numerator: \( -8y + x = -8(2) + (-4) \).
3. Evaluate the absolute value of the numerator: \( | -8y + x | \) using the result from the previous step.
4. Calculate the absolute value of \( x \) in the denominator: \( |x| = |-4| \), then apply the negative sign outside the absolute value.
5. Finally, write the expression as \( \frac{\text{numerator}}{\text{denominator}} \) using the values found, but do not compute the final division.

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, |−3| = 3 and |5| = 5. It is important to apply absolute value correctly, especially when dealing with expressions inside and outside the absolute value symbols.

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. Here, x = -4 and y = 2 are substituted into the expression to evaluate it. Accurate substitution is essential to simplify and correctly compute the expression.

Order of Operations

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