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Chapter 0: Problem 133

Write an inequality representing the given statement. \(b\) is positive.

Short Answer

Expert verified
The inequality is \( b > 0 \).

Step by step solution

01

Understand the Given Statement

The statement says that the variable 'b' is positive. This means that 'b' is greater than zero.
02

Write the Inequality

To write the inequality, simply express that 'b' is greater than zero. In mathematical terms, this is written as: \( b > 0 \)

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Key Concepts

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

Positive Numbers
Positive numbers are numbers greater than zero. They include all the numbers you count, like 1, 2, 3, and so on. They are very different from negative numbers, which are less than zero.

Positive numbers can be whole numbers (integers), fractions, or decimals. For example:
  • Whole numbers: 5, 10, 32
  • Fractions: 3/4, 1/2
  • Decimals: 0.5, 2.75
If a number is described as positive, it is always more than zero. This is crucial when writing and interpreting inequalities, as it helps us understand the range and limitations of the variable.
Writing Inequalities
An inequality compares two values, showing if one is less than, greater than, or sometimes equal to another. In inequalities, we use symbols to show these comparisons.
  • '<': less than
  • '>': greater than
  • '鈮�': less than or equal to
  • '鈮�': greater than or equal to
When the statement says 'b is positive,' we understand that 'b' is greater than zero. In mathematical language, we write this as: \( b > 0 \). This inequality tells us that 'b' must be any number that is not zero but is more than zero. Inequalities can describe many different situations in algebra and help us solve problems where solutions range over many possible values.
Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operations. They represent a value or the relationship between values. Expressions do not have an equality sign, unlike equations.

In the context of inequalities, expressions involve symbols like '<' or '>'. For example, an expression like \( b + 3 > 5 \) shows that the variable 'b' plus three must be more than five.

Here鈥檚 a breakdown:
  • 'b': A variable that represents an unknown number.
  • '+ 3': An operation involving addition.
  • '> 5': Indicates that the result of 'b + 3' must be greater than 5.
When you create expressions, you鈥檙e essentially setting up a condition that needs to be met. This helps in solving problems and understanding the relationships between different quantities.

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Most popular questions from this chapter

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