What is the value of this expression when [tex]g=-3.5[/tex]?
[tex]8-|2 g-5|[/tex]
A. 20
B. 10
C. 6
D. -4
Answer (2)
Substitute g = − 3.5 into the expression 8 − ∣2 g − 5∣ .
Simplify the expression inside the absolute value: 2 ( − 3.5 ) − 5 = − 7 − 5 = − 12 .
Evaluate the absolute value: ∣ − 12∣ = 12 .
Subtract the absolute value from 8: 8 − 12 = − 4 . The final answer is − 4 .
Explanation
Understanding the Problem We are given the expression 8 − ∣2 g − 5∣ and asked to evaluate it when g = − 3.5 . This involves substituting the given value of g into the expression and simplifying. The absolute value function ∣ x ∣ returns the non-negative value of x , so we need to be careful with signs.
Substitution First, substitute g = − 3.5 into the expression: 8 − ∣2 ( − 3.5 ) − 5∣
Simplifying Inside Absolute Value Next, simplify the expression inside the absolute value: 2 ( − 3.5 ) − 5 = − 7 − 5 = − 12
Evaluating Absolute Value Now, evaluate the absolute value: ∣ − 12∣ = 12
Final Calculation Finally, subtract the absolute value from 8: 8 − 12 = − 4
Conclusion Therefore, the value of the expression 8 − ∣2 g − 5∣ when g = − 3.5 is − 4 .
Examples
Absolute value expressions are used in many real-world applications, such as calculating distances or errors. For example, if you are measuring the distance between two points, you might use an absolute value to ensure the distance is always positive, regardless of the order in which you subtract the coordinates. Similarly, in engineering, absolute values are used to calculate tolerances or deviations from a desired value, ensuring that the error is always expressed as a positive quantity.
The value of the expression 8 − ∣2 g − 5∣ when g = − 3.5 is − 4 . Therefore, the correct answer is option D. This is calculated by substituting the value of g into the expression and simplifying step by step.
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