Evaluate $3|-5|-2|-2|$
Answer (2)
Evaluate the absolute values: ∣ − 5∣ = 5 and ∣ − 2∣ = 2 .
Substitute the absolute values into the expression: 3 ( 5 ) − 2 ( 2 ) .
Perform the multiplications: 15 − 4 .
Perform the subtraction: 15 − 4 = 11 . The final answer is 11 .
Explanation
Understanding the Expression We are asked to evaluate the expression 3∣ − 5∣ − 2∣ − 2∣ . This involves absolute values and basic arithmetic operations. Let's break it down step by step.
Evaluating Absolute Values First, we need to evaluate the absolute values. The absolute value of a number is its distance from zero. So, ∣ − 5∣ = 5 and ∣ − 2∣ = 2 .
Substituting Values Now, substitute these values back into the expression: 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 .
Final Answer Therefore, the value of the expression 3∣ − 5∣ − 2∣ − 2∣ is 11 .
Examples
Absolute values are used in many real-world scenarios, such as calculating distances or errors. For example, if you are measuring the distance between two points, you might get a negative value due to the direction, but the actual distance is always positive, which is the absolute value of the measurement. Similarly, in error analysis, the absolute value of the error is more important than the sign of the error.
The value of the expression 3∣ − 5∣ − 2∣ − 2∣ is evaluated step by step, resulting in 11. This is found by calculating the absolute values of the numbers, substituting back into the expression, and performing the arithmetic. The final answer is 11.
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