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

Verified step by step guidance

1. Identify the given expression: \(|-5y + x|\) and the values \(x = -4\) and \(y = 2\).
2. Substitute the values of \(x\) and \(y\) into the expression: \(|-5(2) + (-4)|\).
3. Perform the multiplication inside the absolute value: \(|-10 - 4|\).
4. Simplify the expression inside the absolute value: \(|-14|\).
5. Recall that the absolute value of a number is its distance from zero, so \(|-14| = 14\).

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 first, then multiplication/division, followed by addition/subtraction. Correct application ensures accurate evaluation of expressions.

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, which is essential when evaluating expressions involving absolute value bars.