Problem 65 Evaluate \(|b|-|a|\) if \(a=2\) ... [FREE SOLUTION]

Chapter 2: Problem 65

Evaluate \(|b|-|a|\) if \(a=2\) and \(b=-4\)

Short Answer

Expert verified

The result is 2.

Step by step solution

Substitute Values

First, substitute the given values of the variables into the expression. Replace \(a\) with 2 and \(b\) with -4. The expression becomes \(|-4| - |2|\).

Calculate Absolute Values

Next, calculate the absolute values of \(b\) and \(a\). For \(b = -4\), \(|b| = |-4| = 4\). For \(a = 2\), \(|a| = |2| = 2\).

Subtract Absolute Values

Finally, subtract the absolute value of \(a\) from the absolute value of \(b\). Thus, compute \(4 - 2\), which equals 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Prealgebra

Prealgebra is the foundation of all higher mathematics. It prepares students for algebra by covering basic mathematical concepts. These include arithmetic operations, fractions, and an introduction to equations. This particular exercise involves understanding absolute values.

Absolute value is a measure of the distance a number is from zero on the number line, making it always positive. Understanding this concept is crucial, as it represents a real-world scenario in terms of distance, regardless of direction.

Example: The absolute value of both -3 and 3 is 3.
Notation: The absolute value of a number, say x, is written as \(|x|\).
Usage: Absolute values help in solving equations where only the magnitude of values matters.

Substitution Method

The substitution method is a way to solve equations by replacing variables with provided values. It's a straightforward technique that simplifies expressions and is widely used in various mathematical problems.

In this exercise, substituting the given values of variables makes complex expressions easier to handle. We replace each variable with its corresponding number and perform operations to find a solution.

Application: Substitute variables in an equation with their assigned values.
Benefit: Makes problem-solving more systematic and efficient.
Example: In the expression \(|b|-|a|\), replace 'a' with 2 and 'b' with -4 to compute easily.

Integer Operations

Integer operations involve mathematical calculations with whole numbers, both positive and negative. Mastery of integer operations is crucial for handling real-world problems that involve gains and losses or changes in positions.

In this exercise, we perform operations on integers, specifically subtraction after determining absolute values. It's important to remember:

Addition: Combining the values of integers. \(5 + (-3) = 2\).
Subtraction: Finding the difference between integers. Start with the absolute value, then subtract \(|b| - |a| = 4 - 2\).
Multiplication/Division: Adjust signs accordingly (multiply/divide two negative numbers to get a positive result).

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91影视

Evaluate \(|b|-|a|\) if \(a=2\) and \(b=-4\)

Short Answer

Step by step solution

Substitute Values

Calculate Absolute Values

Subtract Absolute Values

Key Concepts

Prealgebra

Substitution Method

Integer Operations

One App. One Place for Learning.

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