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Difficulty: HardOrder of Operations

If x=−2x = -2, y=24y = 24, and z=−4z = -4, what is the value of the following expression?

−2x3+y∣z∣ -2x^3 + \frac{y}{|z|}
  1. A
    -10
  2. B
    70
  3. 22Answer
  4. D
    10

Answer

The correct answer is 22.
The correct value is found by accurately substituting the negative numbers into the expression. Applying the exponent to -2 yields -8. Multiplying -8 by the coefficient -2 gives 16. Finally, adding the result of 24 divided by the absolute value of -4 (which simplifies to 6) produces 22.

Step-by-Step Solution

1
Substitute the given values into the algebraic expression.
−2(−2)3+24∣−4∣-2(-2)^3 + \frac{24}{|-4|}
Replacing variables with their numerical equivalents is the required first step before evaluating the expression.
2
Evaluate the absolute value in the denominator.
∣−4∣=4|-4| = 4, so the fraction becomes 244\frac{24}{4}.
Absolute value symbols act as grouping symbols, and the absolute value of a negative number is positive.
3
Evaluate the exponent.
(−2)3=−8(-2)^3 = -8, so the expression becomes −2(−8)+244-2(-8) + \frac{24}{4}.
According to the order of operations (PEMDAS), exponents must be evaluated before multiplication.
4
Perform the multiplication and division from left to right.
−2(−8)=16-2(-8) = 16 and 24÷4=624 \div 4 = 6. The expression simplifies to 16+616 + 6.
Multiplication and division share the same priority and are performed before addition.
5
Perform the final addition.
16+6=2216 + 6 = 22
Addition is the final operation remaining in the expression.

Key Concept

Order of Operations with Variable Substitution
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Topics

Order of Operations

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