Problem 86 - Introductory Algebra for College Students

Question

Find the value of each expression. $$-|-8-(-2)|-(-6)$$

Step-by-Step Solution

Answer

The value of the given expression is 12.

Step 1: Resolve Brackets

Firstly, according to BIDMAS/BODMAS order, the arithmetic in the brackets needs to be resolved. As there are two negative signs making the operation in the brackets, they get multiplied and become a positive. Hence, we have: \[|-8 + 2| - (-6)\] which simplifies to \[|-6| - (-6)\]

Step 2: Apply Absolute Value

The next step is to evaluate the absolute value. The absolute value of any number \(a\), denoted by \(|a|\), is always a positive value. If \(a\) is positive or zero, then \(|a|\) is equal to \(a\). If \(a\) is negative, then \(|a|\) is equal to \(-a\). Here, \(-6\) is negative, so its absolute value is \(-(-6)\) or just \(6\). Hence, the expression simplifies to: \[6 - (-6)\].

Step 3: Final Subtraction

The last step is to subtract -6 from 6. Here, two negative signs make a positive. Hence the final computation would be: \[6 + 6 = 12\]