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Chapter 1: Problem 3

Write the given statement as an inequality. $$ a+b \text { is nonnegative } $$

Short Answer

Expert verified
The inequality is \(a+b \geq 0\).

Step by step solution

01

Understand the Statement

The statement "a+b is nonnegative" means that the value of \(a+b\) is either greater than or equal to zero. This concept will guide us to write the inequality appropriately.
02

Translate into Mathematical Inequality

To express "nonnegative" mathematically, we use the inequality symbol \(\geq\). Thus, the statement translates to \(a + b \geq 0\), which means that the sum of \(a\) and \(b\) can be zero or any positive number.

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Key Concepts

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

Nonnegative Numbers
Nonnegative numbers are a vital concept in mathematics, representing any number that is zero or positive. These numbers play a crucial role, especially when dealing with inequalities. In simple terms, a nonnegative number is anything that is not negative.
Some key features of nonnegative numbers include:
  • They are always equal to or greater than zero.
  • They include the set of all positive numbers and zero itself.
  • In inequalities, these numbers are often represented using the symbol \(">=0"\) to indicate their nonnegative nature.
Understanding nonnegative numbers helps you set boundaries in mathematical problems, ensuring values are within acceptable limits, like when calculating lengths, areas, and many real-world scenarios.
Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and symbols that represent a quantity. They serve as the language of mathematics, allowing us to describe relationships and make calculations.
For example, in the expression \(a+b\), both \(a\) and \(b\) are variables that can represent different values.
Key points about mathematical expressions include:
  • They can involve operations such as addition, subtraction, multiplication, and division.
  • Variables stand for unknown or variable values, which may change.
  • Expressions can be evaluated or simplified according to mathematical rules.
When dealing with inequalities, transforming statements into mathematical expressions can help visualize and understand the mathematical relationship at hand.
Solving Inequalities
Solving inequalities involves finding all possible values that satisfy a given inequality condition. These values typically lie within a particular set range.
The process of solving inequalities is somewhat similar to solving equations, but it includes careful consideration of the inequality's direction (">" or "<").
Important steps in solving inequalities:
  • Identify the inequality symbol and understand its meaning.
  • Rewriting the inequality to isolate variables can help to solve it.
  • Remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.
By understanding these rules, you'll be able to handle inequalities effectively, whether it's a simple statement or a more complex problem.

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Most popular questions from this chapter

Use factorization to simplify the given expression in part (a). Then, if instructed, find the indicated limit in part \((b)\). (a) \(\frac{x^{2}-7 x+6}{x-1}\) (b) \(\lim _{x \rightarrow 1} \frac{x^{2}-7 x+6}{x-1}\)

Use factorization to simplify the given expression in part (a). Then, if instructed, find the indicated limit in part \((b)\). (a) \(\frac{x^{3}-1}{x^{2}+3 x-4}\) (b) \(\lim _{x \rightarrow 1} \frac{x^{3}-1}{x^{2}+3 x-4}\)

Find an equation of the circle that satisfies the given conditions. center (4,-5) , graph passes through (7,-3)

Use addition of algebraic fractions to simplify the given expression in part (a). Then, if instructed, find the indicated limit in part (b). (a) \(\frac{1}{x}\left[\frac{1}{9}-\frac{1}{x+9}\right]\) (b) \(\lim _{x \rightarrow 0} \frac{1}{x}\left[\frac{1}{9}-\frac{1}{x+9}\right.\)

Sketch the semicircle defined by the given equation. \(x=1-\sqrt{1-y^{2}}\)
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