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Chapter 4: Problem 12

Let \(a=-2\) and \(b=3 .\) Evaluate each expression. $$|a+b|$$

Short Answer

Expert verified
The value of \(|a+b|\) is 1.

Step by step solution

01

Identify the values of \(a\) and \(b\)

Given the values of \(a\) and \(b\) are -2 and 3 respectively.
02

Calculate the sum

Add \(a\) and \(b\) together. -2 + 3 equals 1.
03

Find the absolute value

The absolute value of the sum is \(|1|\), which is 1.

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Key Concepts

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

Evaluating Expressions
Evaluating expressions is all about simplifying or finding the numerical value of a given mathematical phrase. It involves substituting variables with their values and then carrying out the operations. For instance, in our example, the expression to evaluate is \(|a+b|\). Here, we begin by replacing the variables with their respective values: \(a = -2\) and \(b = 3\).
  • Substitution: Replace \(a\) with \(-2\) and \(b\) with \(3\).
  • Combine: Compute the sum of \(-2\) and \(3\).
  • Final Evaluation: Find the absolute value of the result from the combination.
By following these steps, you can simplify an expression to find its value, which in this case is \(1\). Expression evaluation makes it easier to understand and solve complex algebraic formulas.
Integer Operations
Integer operations are fundamental in algebra and arithmetic, involving adding, subtracting, multiplying, and dividing whole numbers or integers. In the example exercise, we're working with adding integers: \(-2\) and \(3\). Understanding how these operations work is crucial for evaluating expressions correctly.
  • Addition: Combine \(-2\) and \(3\) by following the rules of integer addition.
  • Positive and Negative Integers: When adding a negative and a positive integer, subtract the smaller absolute value from the larger one and keep the sign of the integer with a larger absolute value.
  • Result: Here, \(-2 + 3\) simplifies to \(1\), the positive integer, because the positive value is greater.
Becoming proficient in integer operations helps in tackling more challenging problems in both algebraic and arithmetic contexts.
Basic Algebra
Basic algebra involves understanding the manipulation and simplification of expressions and equations. The exercise and solution provided demonstrate a simple yet essential algebraic concept 鈥� using absolute values in expressions.
  • Variables and Constants: Learn the difference between variables (like \(a\) and \(b\)) and constants, which do not change.
  • Substitution: Replacing variables with actual numbers to solve expressions.
  • Absolute Value: The absolute value \(|x|\) of a number \(x\) is its distance from zero on a number line, always non-negative.
Understand that basic algebra serves as the foundation for more advanced topics and is vital for solving real-world problems using mathematical reasoning.

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Most popular questions from this chapter

Find the difference when \(\left(-3 z^{3}-4 z+7\right)\) is subtracted from the sum of \(\left(2 z^{2}+3 z-7\right)\) and \(\left(-4 z^{3}-2 z-3\right)\)

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