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Chapter 0: Problem 41

Write each statement as an inequality. \(a\) is at least \(5 .\)

Short Answer

Expert verified
a \geq 5

Step by step solution

01

Understand the phrase

The phrase 'at least' means that the value could be greater than or equal to the specified number. Here, 'at least 5' means the value must be 5 or more.
02

Choose the correct inequality symbol

Since 'at least' implies that the value is greater than or equal to, the correct inequality symbol to use is \( \geq \).
03

Formulate the inequality

Combine the variable and the number with the chosen inequality symbol. The variable given is 'a' and the number is 5. Therefore, the inequality is \( a \geq 5 \).

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Key Concepts

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

inequality symbols
Inequality symbols are used in algebra to show the relationship between two values.

  • The most common inequality symbols are:

  • 'Greater than (>)': This means the first value is bigger than the second one.

  • 'Less than (<)': This shows the first value is smaller than the second one.

  • 'Greater than or equal to (鈮�)': This means the first value is bigger than or the same as the second one.

  • 'Less than or equal to (鈮�)': This indicates the first value is smaller than or the same as the second one.


In the given exercise, 'at least' translates to 'greater than or equal to'. Therefore, the correct symbol is '鈮�'. This symbol will represent that a variable can be that number or higher. Understanding these symbols is essential for writing correct inequalities.
algebraic expressions
Algebraic expressions are combinations of numbers, variables, and operations. In the exercise, the variable used is 'a'.

  • A variable represents an unknown value and is often denoted by letters like a, b, x, or y.

  • Numbers can represent constants.

  • Operations include addition, subtraction, multiplication, and division.


When creating inequalities, you bring together all these parts to express a relationship. In our example, the algebraic expression is 'a 鈮� 5'. Here, 'a' is the variable, '5' is the constant, and '鈮�' is the inequality symbol showing the relationship between them. This expression means every value for 'a' that meets the condition will solve the inequality.
mathematical phrases interpretation
Interpreting mathematical phrases allows you to translate words into mathematical expressions or inequalities.
Phrases often indicate specific mathematical relationships:
  • 'At least' means the smallest value is the given number, but it can be larger.

  • 'At most' indicates the value is that number or smaller.

  • 'More than' means the value is larger than the given number.

  • 'Less than' shows the value is smaller than the given number.


To interpret 鈥榓 is at least 5鈥�, determine the smallest value 'a' can be, which is 5. Then conclude that 'a' can be equal to or greater than 5. Thus, 鈥榓t least鈥� translates to '鈮�'. Combine this interpretation with algebraic expressions, and you get 'a 鈮� 5'. Knowing these phrases helps in writing accurate inequalities.

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Most popular questions from this chapter

Multiply and simplify. $$ (2 x-5)(x+4) $$

The total national expenditure for health care has been increasing since the year 2000 . For privately insured individuals in the United States, the following models give the total amount spent for health insurance premiums \(I\) (in \$ billions) and the total amount spent on other out-of-pocket health- related expenses \(P\) (in \$ billions). (Source: U.S. Centers for Medicare \& Medicaid Services, www.census.gov) \(I=45.58 x+460.1 \quad\) Total spent on health insurance premiums \(x\) years since 2000. \(P=10.86 x+191.5 \quad\) Other out-of-pocket health-related expenses \(x\) years since 2000. a. Determine the total expenditure for private health insurance premiums for the year \(2010 .\) b. Determine the total expenditure for other health-related out-of-pocket expenses for the year \(2010 .\) c. Evaluate the polynomial \(I+P\) found in Exercise \(57(\) a) for \(x=10\).

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