Simplify.
26. $|-6-14|$
Answer (1)
Calculate the sum inside the absolute value: − 6 − 14 = − 20 .
Take the absolute value of the result: ∣ − 20∣ = 20 .
The simplified expression is 20 .
Explanation
Understanding the Problem We are asked to simplify the expression ∣ − 6 − 14∣ . This involves finding the absolute value of the result of subtracting 14 from -6.
Calculating the Sum First, we need to calculate the value inside the absolute value symbols: − 6 − 14 = − 20 .
Finding the Absolute Value Next, we take the absolute value of -20. The absolute value of a number is its distance from 0 on the number line, so ∣ − 20∣ = 20 .
Final Answer Therefore, the simplified expression is 20.
Examples
Absolute values are used in many real-world scenarios, such as calculating the magnitude of a change, regardless of direction. For example, if you deposit $100 and then withdraw $150, the net change in your account is - 50. Ho w e v er , i f yo u ′ re in t eres t e d in t h e ma g ni t u d eo f t h ec han g e , yo u w o u l d u se t h e ab so l u t e v a l u e , w hi c hi s |-50| = $50. This tells you the total amount of money that moved in and out of your account, without considering whether it was a deposit or withdrawal. Absolute values are also used in engineering to calculate tolerances or deviations from a specified value.
