Problem 9 - Precalculus

Question

Evaluate each expression. $$|-6+2|-|4|$$

Step-by-Step Solution

Answer

0

Step 1: Evaluate the Inside of the Absolute Value

Start by evaluating the expression inside the first absolute value. The expression is \(-6 + 2\). Calculate \(-6 + 2\) to get \(-4\).

Step 2: Apply Absolute Value

Next, apply the absolute value to the result from Step 1. The absolute value of \(-4\) is \(4\).

Step 3: Evaluate the Second Absolute Value

Now, evaluate the expression inside the second absolute value, which is \(|4|\). Since \(4\) is positive, its absolute value is \(4\).

Step 4: Subtract the Values

Subtract the absolute value calculated in Step 3 from the absolute value calculated in Step 2. Thus, calculate \(4 - 4\) to get \(0\).

Key Concepts

Evaluating Expressions

When dealing with expressions in mathematics, one of the key tasks is to evaluate them. This means finding the value of an expression by performing operations within it according to the rules of mathematics. In the given exercise, we worked with absolute values and basic arithmetic operations, like addition and subtraction.

Evaluating an expression begins with identifying any operations that need to be performed first based on the order of operations. Typically, we evaluate expressions inside parentheses, brackets, or other grouping symbols first, which can include absolute values.

In the provided example, the operations inside the absolute value bars were calculated first. This gives us a clearer expression to work with, by simplifying it step by step and making it easier to find the final result.

Integer Operations

Integer operations involve basic arithmetic operations—such as addition, subtraction, multiplication, and division—using whole numbers, which are integers. Understanding how these operations work is crucial for solving math problems effectively.

In the example, we dealt with integers -6 and 2. When adding these two numbers, consider the rules of integer addition. They state that different signs (negative and positive) require subtraction, while the result takes the sign of the larger absolute value integer. Thus, -6 + 2 = -4.

The final subtraction step involved integers -4 and -4 in their absolute forms, resulting in a calculated difference of 0. Recognizing how integers interact based on their inherent sign (positive or negative) is fundamental to correctly performing operations.

Mathematics Problem Solving

Mathematics problem solving is the process of working through details of a math problem to find the answer. It requires logical reasoning and understanding of math concepts, such as absolute values and operations with integers, to evaluate expressions accurately.

Problem-solving in math often involves breaking down a problem into manageable steps, as was demonstrated in the exercise. First, individual components within absolute values were addressed. Then, their results were calculated and further used in subsequent operations. This sequential approach supports clarity and accuracy in achieving the final solution.

By relying on a structured method, students become better equipped to tackle more complex problems efficiently, linking various math concepts comprehensively to arrive at the correct answer.