Which graph represents the inequality $-3.6 \geq x$?
Answer (2)
The inequality − 3.6 g e x is equivalent to x l e − 3.6 .
The graph representing this inequality has a closed circle at − 3.6 .
The line extends to the left, indicating all values less than or equal to − 3.6 .
The graph includes all values from − 4.5 up to and including − 3.6 . Therefore, the graph represents the solution to the inequality. The graph represents the inequality x ≤ − 3.6
Explanation
Understanding the Inequality We are given the inequality − 3.6 g e x , which can be rewritten as x l e − 3.6 . This means we are looking for all values of x that are less than or equal to − 3.6 . On a number line, this is represented by a closed circle (or a filled-in dot) at − 3.6 , and the line extends to the left (towards smaller values).
Analyzing the Number Line The number line provided ranges from − 4.5 to − 2.7 . We need to identify the graph that includes all values from − 4.5 up to and including − 3.6 .
Identifying the Correct Graph Therefore, the correct graph will have a closed circle at − 3.6 and the line extending to the left, covering all numbers less than or equal to − 3.6 .
Examples
Understanding inequalities is crucial in many real-world scenarios. For example, when setting speed limits on roads, engineers use inequalities to define the range of safe speeds. Similarly, in budgeting, inequalities help determine how much money can be spent on different items while staying within a certain limit. In science, inequalities are used to define acceptable ranges for experimental conditions to ensure accurate and reliable results. These examples show how inequalities are not just abstract mathematical concepts but powerful tools for making informed decisions in everyday life.
The inequality − 3.6 ≥ x translates to x ≤ − 3.6 , and its graph includes a closed circle at − 3.6 with shading extending to the left, indicating all values less than or equal to − 3.6 . This visual representation is essential for understanding the solution set. For example, values like − 4.0 are included since they satisfy the inequality.
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