Problem 82 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(\frac{-8-|-3+2|}{-3-(-6)}\)

Step-by-Step Solution

Answer

\frac{-6}{-7}

Step 1 - Simplify Inside the Absolute Value

First, simplify the expression inside the absolute value: . Calculate Simplifying gives us .

Step 2 - Evaluate the Absolute Value

Now, solve the absolute value: .

Step 3 - Perform the Subtraction in the Numerator

Replace the absolute value with its result and perform the subtraction in the numerator: .

Step 4 - Simplify the Denominator

Simplify the operation in the denominator: .

Step 5 - Perform the Division

Now that both numerator and denominator are simplified, perform the division to get the final result: .

Key Concepts

absolute value

Absolute value refers to the distance of a number from zero on the number line, regardless of direction. It's always a non-negative number.

For example, the absolute value of -3 is 3, written as \(|-3| = 3\). The same applies to positive numbers, where \( |3| = 3\).

In the given exercise, we first simplify the expression inside the absolute value:

• -3 + 2 = -1

Then, we take the absolute value of -1, which is 1:

• |-1| = 1

simplifying expressions

Simplifying expressions is about reducing them to their most basic form. This makes them easier to work with.

Steps for simplifying the given expression:

• Calculate inside the absolute value first: -3 + 2 = -1
• Take the absolute value: -1 becomes 1
• Replace this result back into the expression

After these steps, our expression becomes \(\frac{-8-1}{-3-(-6)} \).

division

Division is the process of determining how many times one number is contained within another. In algebra, we also use it to simplify expressions.

• Identify the numerator and the denominator. Here, the numerator is -9 and the denominator is 3.
• Perform the division operation: \(\frac{-9}{3} = -3\).

By dividing -9 by 3, we simplify the expression to -3.

subtraction

Subtraction is the operation of finding the difference between numbers. In this exercise, we use subtraction in both the numerator and the denominator.

• For the numerator: -8 - 1 = -9
• For the denominator: -3 - (-6) = -3 + 6 = 3

The subtraction operations lead us to the simplified fraction \(\frac{-9}{3} \).