Consider the algebraic expression \frac{2x^2 - yz}{x + y}. If the variables are assigned t… — Armed Services Vocational Aptitude Battery (ASVAB)

Consider the algebraic expression $\frac{2x^2 - yz}{x + y}$ . If the variables are assigned the values $x = -3$ , $y = 5$ , and $z = -2$ , what are the intermediate evaluated values for the numerator and denominator, and what is the final result?

Answer:After substituting the values, the evaluated result of the numerator is 【28】 and the denominator is 【2】. Dividing these intermediate values yields a final result of 【14】.

Answer

The intermediate numerator evaluates to 28, the denominator to 2, and the final evaluated result is 14.

The correct final value is 14. This is determined by carefully substituting the negative and positive variable values into the numerator and denominator, strictly applying the order of operations to handle exponents and negative signs, and finally dividing the intermediate numerator 28 by the denominator 2.

Step-by-Step Solution

Substitute the value of

x

into the first term of the numerator,

2x^2

2(-3)^2 = 2(9) = 18

Applying the order of operations, exponentiation must be evaluated before multiplication.

Substitute the values of

y

and

z

into the second term of the numerator,

yz

(5)(-2) = -10

Multiplying a positive integer by a negative integer results in a negative integer.

Calculate the complete numerator by subtracting the second term from the first.

18 - (-10) = 18 + 10 = 28

Subtracting a negative number is mathematically equivalent to adding its positive counterpart.

Substitute the values of

x

and

y

to evaluate the denominator,

x + y

-3 + 5 = 2

Combining the negative and positive integers.

Divide the fully evaluated numerator by the evaluated denominator.

\frac{28}{2} = 14

The final step in evaluating the rational expression.

Key Concept

Evaluating Algebraic Expressions

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic