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Chapter 1: Problem 82

Write each statement in words and decide whether it is true or false. $$ 6 \geq 12 $$

Short Answer

Expert verified
6 is not greater than or equal to 12. False.

Step by step solution

01

- Understand the Inequality Symbol

Identify the inequality symbol in the statement. The symbol \( \geq \) denotes 'greater than or equal to'.
02

- Read the Statement in Words

Translate the inequality \(6 \geq 12\) into words. This statement reads: '6 is greater than or equal to 12.'
03

- Analyze the Mathematical Statement

Compare the numbers. Determine whether 6 is greater than or equal to 12. Since 6 is less than 12, this statement is false.

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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 crucial in algebra for comparing two values. These symbols include less than \((<)\), less than or equal to \((leq)\), greater than \((>)\), and greater than or equal to \(( geq)\). These symbols help us determine relationships between numbers, such as which number is larger or smaller. For instance, the symbol \((\leq)\) means the number on the left is either less than or equal to the number on the right. Understanding how to read and interpret these inequality symbols is essential for analyzing mathematical statements accurately.
greater than or equal to
The inequality symbol \((\geq)\) stands for 'greater than or equal to' and is used to compare two values. When you see this symbol, it means the value on the left is either larger than or exactly the same as the value on the right. In the example provided, the statement \(6 \geq 12\) translates to '6 is greater than or equal to 12'. To determine if this statement is true, compare the values directly. Since 6 is neither greater nor equal to 12, the statement is false.
analyzing mathematical statements
Analyzing mathematical statements involves understanding and interpreting the relationships represented by inequality symbols. Begin with translating the mathematical statement into words. For \(6 \geq 12\), it means '6 is greater than or equal to 12'. Next, compare the actual numbers to verify the statement's truthfulness. Is 6 larger than or equal to 12? Clearly, 6 is smaller than 12, making the statement false. Regular practice with various inequalities helps build confidence and accuracy in interpreting mathematical expressions correctly.

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Most popular questions from this chapter

The two tables show the heights of some selected mountains and the depths of some selected trenches. Use the information given to answer. \( \)\begin{array}{|l|c|}\hline \text { Mountain } & {\text { Height (in feet) }} \\\ {\text { Foraker }} & {17,400} \\ {\text { Wilson }} & {14,246} \\\ {\text { Pikes Peak }} & {14,110} \\ \hline\end{array} $$ \begin{array}{|l|c|}\hline\text {} & {\text { Depth }( \text { in feet } } \\ {\text { Trench }} & {\text { as a negative number }} \\ {\text { Philippine }} & {-32,995} \\ {\text { Cayman }} & {-24,721} \\ {\text { Java }} & {-23,376} \\ \hline \end{array} $$ How much deeper is the Philippine Trench than the Cayman Trench?

Solve each problem. The largest change in temperature ever recorded within a 24 -hr period occurred in Montana, on January \(23-24,1916\). The temperature fell \(100^{\circ} \mathrm{F}\) from a starting temperature of \(44^{\circ} \mathrm{F} .\) What was the low temperature during this period?

Write a numerical expression for each phrase and simplify. \(-2\) added to the sum of \(-18\) and 11

Write a numerical expression for each phrase and simplify. The sum of \(-3\) and 5 and \(-12\)

Find each difference. $$ \frac{9}{10}-\left(\frac{1}{8}-\frac{3}{10}\right) $$
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