Textbook Question
Evaluate each expression for x = -4 and y = 2. |-3x + 4y|
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0. Review of Algebra
Algebraic Expressions
1:38 minutesProblem 149
Textbook Question
Evaluate each expression for x = -4 and y = 2. |-8y + x| / -|x|
Verified step by step guidance1
First, substitute the given values of \( x = -4 \) and \( y = 2 \) into the expression \( \frac{| -8y + x |}{- |x|} \).
Calculate the expression inside the absolute value in the numerator: \( -8y + x = -8(2) + (-4) \).
Evaluate the absolute value of the numerator: \( | -8y + x | \) using the result from the previous step.
Calculate the absolute value of \( x \) in the denominator: \( |x| = |-4| \), then apply the negative sign outside the absolute value.
Finally, write the expression as \( \frac{\text{numerator}}{\text{denominator}} \) using the values found, but do not compute the final division.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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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.
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