Evaluate $3|-5|-2|-2|$
Answer (1)
The problem requires evaluating the expression 3∣ − 5∣ − 2∣ − 2∣ . The absolute values are ∣ − 5∣ = 5 and ∣ − 2∣ = 2 . Substituting these values gives 3 ( 5 ) − 2 ( 2 ) . Performing the multiplications gives 15 − 4 . Finally, the subtraction yields the answer: 11 .
Explanation
Understanding the Problem We are asked to evaluate the expression 3∣ − 5∣ − 2∣ − 2∣ . This involves understanding the absolute value of numbers and performing basic arithmetic operations.
Evaluating Absolute Values First, we need to evaluate the absolute values. The absolute value of a number is its distance from zero. Therefore, ∣ − 5∣ = 5 and ∣ − 2∣ = 2 .
Substituting Values Now, substitute these values back into the original expression: 3∣ − 5∣ − 2∣ − 2∣ = 3 ( 5 ) − 2 ( 2 ) .
Performing Multiplications Next, perform the multiplications: 3 ( 5 ) = 15 and 2 ( 2 ) = 4 . So the expression becomes 15 − 4 .
Performing Subtraction Finally, perform the subtraction: 15 − 4 = 11 . Therefore, the value of the expression is 11.
Examples
Understanding absolute values is crucial in many real-world scenarios. For instance, when dealing with temperature changes, we often care about the magnitude of the change, regardless of whether it's an increase or decrease. Similarly, in financial analysis, absolute values can represent the magnitude of gains or losses. For example, if an investment decreases by 5 , w ec an s a y t h e ab so l u t ec han g e i s |-5| = $5. This concept helps us focus on the size of the change rather than its direction, providing a clearer picture of the overall impact.
