Evaluate each expression for $x=-4$ and $y=2$.
$\mid 2x-5y\mid$

Verified step by step guidance

1. Substitute the given values of \( x = -4 \) and \( y = 2 \) into the expression \( |2x - 5y| \). This means replacing \( x \) with \( -4 \) and \( y \) with \( 2 \) in the expression.
2. Rewrite the expression with the substituted values: \( |2(-4) - 5(2)| \).
3. Perform the multiplication inside the absolute value: calculate \( 2 \times (-4) \) and \( 5 \times 2 \) separately.
4. Simplify the expression inside the absolute value by combining the results from the multiplications: \( |-8 - 10| \).
5. Evaluate the absolute value by finding the distance of the number inside from zero, which means taking the positive value of the result inside the absolute value bars.

Key Concepts

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. In this problem, x and y are replaced by -4 and 2 respectively, allowing evaluation of the expression with specific numbers.

Order of Operations

The order of operations dictates the sequence in which parts of an expression are calculated, typically parentheses, exponents, multiplication/division, and addition/subtraction. Correctly applying this ensures accurate evaluation of expressions like 2x - 5y.

Absolute Value

Absolute value represents the distance of a number from zero on the number line, always yielding a non-negative result. For example, | -3 | equals 3, so after evaluating 2x - 5y, taking the absolute value ensures the final answer is non-negative.