Examkin

Question

Difficulty: HardEvaluating Algebraic Expressions

Given the variable assignments x=−4x = -4, y=2y = 2, and z=−6z = -6, which of the following represents the evaluated result of the mathematical expression below?

x2y−∣x−z∣y+x x^2 y - \frac{|x - z|}{y + x}
  1. 33Answer
  2. B
    -31
  3. C
    -15
  4. D
    31

Answer

33
Substituting the given values into the expression yields (−4)2(2)−∣−4−(−6)∣2+(−4)(-4)^2(2) - \frac{|-4 - (-6)|}{2 + (-4)}. Squaring −4-4 gives 1616, and multiplying by 22 results in 3232. Inside the absolute value, −4−(−6)-4 - (-6) becomes −4+6=2-4 + 6 = 2, so the numerator is 22. The denominator is 2+(−4)=−22 + (-4) = -2. The fraction simplifies to 2/−2=−12 / -2 = -1. Subtracting this from the first term gives 32−(−1)=3332 - (-1) = 33.

Step-by-Step Solution

1
Substitute the given values for x, y, and z into the expression.
(−4)2(2)−∣−4−(−6)∣2+(−4)(-4)^2 (2) - \frac{|-4 - (-6)|}{2 + (-4)}
Direct substitution is the first requirement to evaluate an algebraic expression.
2
Evaluate the first term with exponents and multiplication.
(−4)2=16(-4)^2 = 16, then 16×2=3216 \times 2 = 32.
Following the order of operations (PEMDAS), exponents are calculated before multiplication.
3
Simplify the expression inside the absolute value in the numerator.
∣−4−(−6)∣=∣−4+6∣=∣2∣=2|-4 - (-6)| = |-4 + 6| = |2| = 2.
Subtracting a negative is equivalent to adding a positive. Absolute value makes the result positive.
4
Simplify the denominator and evaluate the fraction.
Denominator is 2+(−4)=−22 + (-4) = -2. The fraction evaluates to 2−2=−1\frac{2}{-2} = -1.
The operations within the implied grouping of the fraction must be fully resolved before dividing.
5
Subtract the evaluated fraction from the first term.
32−(−1)=32+1=3332 - (-1) = 32 + 1 = 33.
Final subtraction, ensuring that subtracting a negative value is treated as addition.

Key Concept

Evaluating Complex Algebraic Expressions with Integers
Rate this question

Topics

Evaluating Algebraic Expressions

More questions from this topic