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

Verified step by step guidance

1. Substitute the given values of \( x = -4 \) and \( y = 2 \) into the expression \( |-3x + 4y| \). This means replacing \( x \) with \( -4 \) and \( y \) with \( 2 \) in the expression.
2. Rewrite the expression after substitution: \( |-3(-4) + 4(2)| \).
3. Simplify inside the absolute value by performing the multiplication: calculate \( -3 \times -4 \) and \( 4 \times 2 \).
4. Add the results from the multiplications inside the absolute value to get a single number.
5. Finally, evaluate the absolute value of the resulting number, which means taking the non-negative value of that number.

Key Concepts

Substitution in Algebraic Expressions

Substitution involves replacing variables in an expression with given numerical values. This step is essential to evaluate the expression for specific values of x and y, allowing simplification to a numerical result.

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). Correct application ensures accurate simplification of expressions.

Absolute Value

Absolute value represents the distance of a number from zero on the number line, always yielding a non-negative result. When evaluating expressions with absolute value, the final answer is the positive magnitude regardless of the sign inside.