Problem 29 - Applied Mathematics: For the Managerial, Life, and Social Sciences

Question

Evaluate the expression. $$ |-6+2| $$

Step-by-Step Solution

Answer

The expression \(|-6+2|\) evaluates to 4 after performing the operation inside the absolute value and taking the absolute value of the result.

Step 1: Evaluate the expression inside the absolute value

We need to evaluate |-6+2|, so first, let's solve the -6 + 2 part: \(-6 + 2 = -4\).

Step 2: Take the absolute value of the result

Now, we have \(|-4|\), so the absolute value of -4 is simply 4. Thus, the expression \(-|6+2|\) evaluates to 4.

Key Concepts

Expression Evaluation

When evaluating an expression, it's crucial to follow the correct order of operations to reach the correct result. In \(|-6+2|\), our task is twofold: - First, handle the operations inside the expression. - Second, apply the absolute value function.To start, remember that absolute value functions take the non-negative value of the number in question. First, though, let's focus on what's inside: the expression \(-6 + 2\). Calculating \(-6 + 2\), simplifies to \(-4\). Expression evaluation often involves simplifying expressions first, before proceeding with any further operations.

Mathematical Operations

In mathematical expressions, operations define how numbers interact with each other. Here, we are focusing on the operations of addition and absolute value.

• **Addition**: Let's simplify \(-6 + 2\). Start from the left to the right, and compute step by step. It's straightforward but easy to make mistakes, so ensure accuracy by double-checking your math.
• **Absolute Value**: Once you have the sum, consider the absolute value. The sign of the number doesn't matter here as absolute value is always positive. Applying absolute value to \(-4\), you simply transform it to \(4\), because absolute values convert negative numbers into positive equivalents. In this expression, these operations interact in a sequence, highlighting a basic yet essential framework of arithmetic, where you simplify inside brackets first and then apply the absolute effect.

Problem Solving Steps

Effective problem solving requires following a series of logical steps. These steps help break down complex tasks into doable parts. For the expression \(|-6+2|\), the steps were clear:1. **Simplify Inside the Absolute**: Always evaluate the expression inside the absolute value first. Here it's \( -6 + 2 = -4\). 2. **Apply the Absolute Value**: After obtaining the result from step 1, take the absolute value. - The absolute value of \(-4\) is \(4\), thus completing the evaluation.This methodical approach ensures that each part of the expression is dealt with in the correct order, maximizing accuracy and understanding. By systematically simplifying first and then applying mathematical functions, problems become more manageable and solutions clearer.