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Chapter 0: Problem 16

Replace the question mark by \(<,>,\) or \(=\), whichever is correct. \(5 ? 6\)

Short Answer

Expert verified
5 < 6

Step by step solution

01

Understand the Comparison

We need to determine if the number 5 is less than, greater than, or equal to the number 6.
02

Compare the Numbers

Compare the two numbers: 5 and 6. Since 5 has a lower value compared to 6, it means 5 is less than 6.
03

Choose the Correct Symbol

The correct symbol to use in the inequality is the 'less than' symbol, which is '<'. So the equation becomes: 5 < 6.

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Key Concepts

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

comparison of numbers
When comparing two numbers, you need to understand the relative value of each number.
This helps you determine if one number is smaller, larger, or equal to the other number.
Imagine you have two numbers, like 5 and 6. To compare them, you look at their values to see which one is larger.
If you visualize numbers on a number line, the number further to the right is the larger number.
For example, 5 is to the left of 6 on the number line, showing that 5 is smaller than 6.
Understanding this arrangement makes comparison easier.
Being able to compare numbers is a critical skill in math. You use it from simple arithmetic to more advanced topics.
less than symbol
When you find out that one number is smaller than another, you use the 'less than' symbol (<) to show this relationship.
The 'less than' symbol looks like an arrow pointing to the left: <. It narrows down, almost like it is pointing towards the smaller number.
So, if you are comparing 5 and 6, you write it as: 5 < 6.
This shows that 5 is less than 6.
Remembering this symbol is important. You use it often when solving inequalities and comparing values.
inequality symbols
Inequality symbols help you compare the size of two numbers. There are several of them:
  • 'Greater than' symbol (>) is used when one number is larger than the other.
  • 'Less than' symbol (<) is used when one number is smaller than the other.
  • 'Equal to' symbol (=) is used when two numbers are the same.
  • 'Greater than or equal to' (鈮�) means a number is bigger or the same as another.
  • 'Less than or equal to' (鈮�) means a number is smaller or the same as another.

Using the right symbol is crucial for accurately expressing relationships between numbers.
For instance, in the example 5 ? 6, we solved it by using the 'less than' symbol. Thus, 5 < 6 is the correct expression.
Understanding these symbols and their meanings will help you handle various mathematical problems with ease.

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Most popular questions from this chapter

Determine which of the values (a) through (d), if any, must be excluded from the domain of the variable in each expression. (a) \(x=0\) (b) \(x=1\) (c) \(x=0\) (d) \(x=-1\) \(\frac{x^{3}}{x^{2}-1}\)

Find the volume \(V\) and surface area \(S\) of a closed rectangular box with length 9 inches, width 4 inches, and height 8 inches.

Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. $$ (x-2 y)(x+y) $$

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime. $$ 1-8 x^{2}-9 x^{4} $$

Simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not \(0 .\) \(\left(\frac{2 x^{-3}}{3 y^{-1}}\right)^{-2}\)
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