Problem 85 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. $$ |-5-6|+|9+2| $$

Step-by-Step Solution

Answer

22

Step 1: Simplify the expression inside the first absolute value

First, solve the expression inside the absolute value: \[-5 - 6\] This simplifies to: \[-11\]

Step 2: Calculate the absolute value

Next, find the absolute value of -11: \[|-11| = 11\]

Step 3: Simplify the expression inside the second absolute value

Now, solve the expression inside the second absolute value: \[9 + 2\] This simplifies to: \[11\]

Step 4: Calculate the second absolute value

Find the absolute value of 11: \[|11| = 11\]

Step 5: Add the results

Add the results of the absolute values: \[11 + 11 = 22\]

Key Concepts

Simplifying Expressions

When tackling mathematical problems, it's vital to break down expressions into simpler forms before diving into more complex operations. In our exercise, we simplify expressions inside absolute value brackets before evaluating them.

Take the expression \(-5 - 6\).
The first step is to perform the subtraction inside the absolute value bracket. Here, subtracting 6 from -5 results in \(-11\).
Simplifying expressions makes it easier to follow the next steps of our calculation, ensuring clarity and accuracy.

Evaluating Absolute Values

Absolute values represent the distance from zero on a number line, regardless of direction. In simple terms, they are always non-negative.

For instance, the absolute value of \(-11\) is calculated as \(|-11|\), which equals \11\. Absolute values essentially strip away the negative sign.
In the given problem, after simplifying the expressions inside the absolute value brackets, we get to evaluate two numbers: \(-11\) and \11\. Their absolute values are both \11\.
Precise evaluation of absolute values is essential as it ensures each number is correctly interpreted in its simplest non-negative form.

Addition of Integers

Once we've simplified and evaluated absolute values, the final step involves the addition of these integers.
The problem at hand requires summing the absolute values of \(-11\) and \11\, both of which equal \11\.
Add these together: \11 + 11\.
The result is \22\.
Addition of integers, especially when derived from absolute values, demands careful attention to ensure all preceding simplifications and evaluations are correctly handled.