Textbook Question
Evaluate each expression for x = -4 and y = 2. |3x - 2y|
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0. Review of Algebra
Algebraic Expressions
1:34 minutesProblem 147
Textbook Question
Evaluate each expression for x = -4 and y = 2. 2|y| - 3|x| / |xy|
Verified step by step guidance1
First, substitute the given values into the expression: replace \( x \) with \( -4 \) and \( y \) with \( 2 \) in the expression \( 2|y| - \frac{3|x|}{|xy|} \).
Calculate the absolute values: find \( |y| \), \( |x| \), and \( |xy| \). Remember that the absolute value of a number is its distance from zero, so it is always non-negative.
Rewrite the expression with the absolute values calculated: \( 2|y| - \frac{3|x|}{|xy|} \) becomes \( 2 \times |2| - \frac{3 \times | -4 |}{|(-4)(2)|} \).
Perform the multiplications and division inside the expression step-by-step: multiply \( 2 \times |2| \), multiply \( 3 \times | -4 | \), and then divide by \( |(-4)(2)| \).
Finally, subtract the fraction from the product \( 2|y| \) to get the simplified expression value.
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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, |x| equals x if x is positive or zero, and -x if x is negative. This concept is essential for correctly evaluating expressions involving absolute values.
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Substitution of Variables
Substitution involves replacing variables in an expression with given numerical values. Here, x and y are replaced with -4 and 2 respectively, allowing the expression to be evaluated numerically. Accurate substitution is crucial for solving algebraic expressions.
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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). Applying this correctly ensures the expression is simplified accurately, especially when fractions and absolute values are involved.
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