The statement below is true.
[tex]$-6.9<-3.4$[/tex]
Select the statement that is equivalent to [tex]$-6.9<-3.4$[/tex].
A. -3.4 is less than -6.9.
B. -6.9 is greater than -3.4.
C. -6.9 is further to the right on the number line than -3.4.
D. -6.9 is further to the left on the number line than -3.4.
Answer (2)
The problem states that − 6.9 < − 3.4 .
We analyze each option to find the equivalent statement.
Option 1 ( − 3.4 < − 6.9 ) is incorrect.
Option 2 ( -3.4"> − 6.9 > − 3.4 ) is incorrect.
Option 3 ( − 6.9 is to the right of − 3.4 ) is incorrect.
Option 4 ( − 6.9 is to the left of − 3.4 ) is correct, as it means − 6.9 < − 3.4 .
The equivalent statement is: − 6.9 is further to the left on the number line than − 3.4 .
Explanation
Understanding the Inequality We are given the inequality − 6.9 < − 3.4 , which states that -6.9 is less than -3.4. We need to find an equivalent statement from the given options.
Analyzing the Options Let's analyze each option:
'-3.4 is less than -6.9' translates to − 3.4 < − 6.9 . This is the opposite of the given inequality, so it's incorrect.
'-6.9 is greater than -3.4' translates to -3.4"> − 6.9 > − 3.4 . This is also the opposite of the given inequality, so it's incorrect.
'-6.9 is further to the right on the number line than -3.4'. On the number line, numbers increase as we move to the right. So, this statement means -3.4"> − 6.9 > − 3.4 , which is incorrect.
'-6.9 is further to the left on the number line than -3.4'. On the number line, numbers decrease as we move to the left. So, this statement means − 6.9 < − 3.4 , which is the same as the given inequality. Therefore, this is the correct statement.
Conclusion The equivalent statement to − 6.9 < − 3.4 is '-6.9 is further to the left on the number line than -3.4'.
Examples
Understanding inequalities like − 6.9 < − 3.4 helps us compare temperatures, bank balances, or even scores in a game. For example, if the temperature outside is -6.9 degrees Celsius and the temperature inside is -3.4 degrees Celsius, the inequality tells us that it's colder outside than inside. Similarly, if you owe $6.90 and your friend owes $3.40, you owe less than your friend (since both are negative values).
The equivalent statement to − 6.9 < − 3.4 is that '-6.9 is further to the left on the number line than -3.4.' This means that − 6.9 is less than − 3.4 . The correct answer is Option D.
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