Let's go through the task of plotting and analyzing the relationship between -4 and -3 step by step.
1. Plotting -4:
- On a number line, 0 is generally the central reference point.
- Numbers to the left of zero are negative, and numbers to the right are positive.
- -4 would be placed to the left of 0.
- The exact location doesn't require great precision here, but you should ensure -4 is plotted further left than -3.
2. Understanding Inequality:
- The statement [tex]$4 > 3$[/tex] is true because 4 is indeed greater than 3.
- When dealing with the negative counterparts of these numbers, the direction of the inequality changes.
3. Analyzing Relationships:
- The inverse of a statement reverses the action. For [tex]$4 > 3$[/tex], the negative counterparts are -4 and -3, respectively.
- When reversing both numbers to their negative counterparts, -4 and -3, the greater number (in magnitude) becomes smaller in value because it is more negative.
Here are the checks for the inequalities:
- [tex]$-4 < -3$[/tex]:
- The inequality changes direction because -4 is indeed less than -3 on a number line.
- Hence, [tex]$-4 < -3$[/tex] is true.
- [tex]$-4 > -3$[/tex]:
- This statement would be incorrect because -4 is not greater than -3. On the contrary, it is less.
- Hence, [tex]$-4 > -3$[/tex] is false.
- [tex]$-4 = -3$[/tex]:
- This statement is also incorrect because -4 and -3 are different numbers.
- Hence, [tex]$-4 = -3$[/tex] is false.
True statement: [tex]$-4 < -3$[/tex]
In conclusion, the correct relationship when comparing -4 to -3 is [tex]$-4 < -3$[/tex]. Therefore, this is the statement that accurately describes the relationship between -4 and -3 based on the context provided.
