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Chapter 1: Problem 79

Write each statement in words and decide whether it is true or false. $$ 5 \neq 8 $$

Short Answer

Expert verified
The statement '5 is not equal to 8' is true.

Step by step solution

01

Title - Translate the Mathematical Statement

First, translate the given mathematical statement into words. The statement is: \( 5 eq 8 \). This translates to '5 is not equal to 8'.
02

Title - Decide the Truth Value

Next, determine whether the translated statement is true or false. '5 is not equal to 8' is indeed a true statement because the number 5 and the number 8 are different.

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Key Concepts

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

Translating Mathematical Statements
Understanding how to translate mathematical statements into words is crucial in algebra. It helps make sense of the symbols and their relationships. When you see an equation or inequality, the first step is to read it as a sentence.
Take the example given in the exercise:
\(5 eq 8\)
This translates to '5 is not equal to 8'.
Let鈥檚 look at some basic translations for a better grasp:
  • \(x + y = 10\) translates to 'The sum of x and y is 10'.
  • \(a < b\) translates to 'a is less than b'.
  • \(z eq 3\) translates to 'z is not equal to 3'.

These translations help turn abstract symbols into understandable language.
Inequality Symbols
Inequality symbols are used to show the relationship between values that are not strictly equal. Here are the most common ones:
  • \(<\) means 'less than'.
  • \(\leq\) means 'less than or equal to'.
  • \(>\) means 'greater than'.
  • \(\geq\) means 'greater than or equal to'.
  • \(eq\) means 'not equal to'.

In our exercise, we used \(eq\) which translates to 'not equal to'. This helps us understand whether two values or variables are different from each other.
Recognizing and using these symbols correctly can make solving inequalities a lot easier.
Truth Value of Mathematical Expressions
Determining the truth value of a mathematical expression is about checking if the statement is true or false. This step is critical for validating solutions.
For example, in the given exercise the statement was:
\(5 eq 8\)
We translated this to '5 is not equal to 8'. Since 5 is indeed different from 8, the statement is true.
Here are some tips to determine the truth value:
  • Compare the numbers directly, like in our example.
  • For algebraic statements, substitute values for variables and simplify the expression.
  • Check logical consistency. An equality like \(7 > 2\) is always true, while \(10 < 4\) is false.

Understanding the truth value helps in verifying the correctness of mathematical solutions.

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Most popular questions from this chapter

A manufacturer has fixed costs of \(\$ 1000\) to produce widgets. Each widget costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(y\) gadgets.

Solve each problem. Bruce Buit also enjoys playing Triominoes. On five successive turns, his scores were \(-13,15,-12,24,\) and \(14 .\) What was his total score for the five turns?

Perform each indicated operation. $$ \left(-\frac{1}{2}+0.25\right)-\left(-\frac{3}{4}+0.75\right) $$

Write a numerical expression for each phrase and simplify. 9 less than \(-13\)

Solve each problem. In \(1998,\) undergraduate college students had an average (mean) credit card balance of 1879. The average balance increased \(\$ 869\) by 2000 , then dropped \(\$ 579\) by \(2004,\) and then increased \(\$ 1004\) by \(2008 .\) What was the average credit card balance of undergraduate college students in \(2008 ?\)
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