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Chapter 0: Problem 49

Determine whether the statement is true or false. $$6.7 \geq 6.7$$

Short Answer

Expert verified
True

Step by step solution

01

- Understand the Symbols

The symbol '鈮�' means 'greater than or equal to'. It indicates that the number on the left is either greater than or equal to the number on the right.
02

- Compare the Numbers

Compare the two numbers on either side of the '鈮�' symbol. In this case, both numbers are 6.7.
03

- Determine Equality

Since both numbers are the same (6.7 = 6.7), the statement 6.7 鈮� 6.7 is true because 6.7 is equal to 6.7.

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Key Concepts

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

Greater Than or Equal To
In algebra, the symbol '鈮�' stands for 'greater than or equal to.' It is used to compare two numbers or expressions to determine their relationship. When we see the symbol '鈮�,' we need to check if the number on the left side is either larger than or exactly the same as the number on the right side.
Let's break it down with an example: if we have 8 鈮� 5, this is true because 8 is greater than 5.
If we have 7 鈮� 7, this is also true because 7 is equal to 7. The 'greater than or equal to' symbol is very important in inequalities because it allows for equality, not just a comparison of greater value.
Comparing Numbers
Comparing numbers involves looking at two values and determining their relationship. With the statement 6.7 鈮� 6.7, let's break down the comparison process:
First, identify the two numbers you are comparing, which in this case are both 6.7.
Next, determine the relationship between these two numbers. Are they the same, or is one greater than the other?
In this situation, both numbers are identical, which leads us to the final step: checking the symbol. With '鈮�', we see that 6.7 is indeed equal to 6.7, making the statement true.
Remember, the symbol helps us understand if we are looking for greater or equal values, not just one specific type.
Equality in Algebra
Equality in algebra means that two values or expressions are the same. The concept is simple but foundational to many algebraic operations and statements. In our example, we have the equation 6.7 = 6.7 inside the inequality 6.7 鈮� 6.7. Since both sides of our equation are equal, it confirms that our statement is true.
When working with inequalities, always look for whether the numbers or expressions could be equal. This is a quick way to verify if an inequality like 鈥樷墺鈥� is true or false.
Understanding equality can help solve more complex problems where you need to balance equations or compare different expressions.

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Most popular questions from this chapter

A polynomial in the variable \(x\) is defined as an expression of the form \(a_{n} x^{n}+a_{n-1} x^{n-1}+a_{n-2} x^{n-2}+\cdots+a_{1} x+a_{0} .\) Explain what this means.

Multiply and simplify. Assume that all variable expressions represent positive real numbers. $$ \left(5 a^{2} \sqrt{b}+7 b^{2} \sqrt{a}\right)^{2} $$

Multiply and simplify. Assume that all variable expressions represent positive real numbers. $$ (2 v-\sqrt{17})^{2} $$

Multiply and simplify. Assume that all variable expressions represent positive real numbers. $$ (\sqrt{y+2}-4)^{2} $$

Simplify each expression. $$ (x-4)^{2}-6(x+1)^{2} $$
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