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 = − 12 .
Evaluate the absolute value: ∣ − 12∣ = 12 .
Substitute the absolute value back into the expression: 8 − 12 = − 4 . The final answer is − 4 .
Explanation
Understanding the problem We are given the expression 8 − ∣2 g − 5∣ and asked to find its value when g = − 3.5 . We will substitute the value of g into the expression and simplify.
Substitution First, substitute g = − 3.5 into the expression: 8 − ∣2 ( − 3.5 ) − 5∣
Simplifying inside the absolute value Next, simplify the expression inside the absolute value: 2 ( − 3.5 ) − 5 = − 7 − 5 = − 12
Evaluating the absolute value Now, evaluate the absolute value: ∣ − 12∣ = 12
Final calculation Finally, substitute the absolute value back into the expression: 8 − ∣2 g − 5∣ = 8 − 12 = − 4
Examples
Absolute value expressions are used in many real-world applications, such as calculating the margin of error in measurements or determining the deviation from a target value in manufacturing processes. For example, if a machine is supposed to cut a metal rod to 10 cm, the absolute value expression can be used to calculate the difference between the actual length and the target length, i.e., ∣10 − a c t u a l _ l e n g t h ∣ . This helps in quality control to ensure that the rods are within acceptable tolerance limits.
The value of the expression 8 − ∣2 g − 5∣ when g = − 3.5 is − 4 . Hence, the correct answer is option D. -4.
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