Many students struggle with solving inequalities, but understanding the solution set of an inequality can be a great way to make progress. An inequality is a mathematical statement that is used to compare two values. It usually involves one of the following symbols: greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤). In this article, the focus will be on the solution set of the inequality 5x-9 ≤ 21.
What is the Solution Set?
The solution set of an inequality is the set of values for the variable that make the inequality true. In this case, the solution set of 5x-9 ≤ 21 is the set of values for x that make 5x-9 ≤ 21 true. To find the solution set, we must first solve the inequality. This can be done by subtracting 9 from both sides of the inequality, which gives us 5x ≤ 30. Then, divide both sides of the inequality by 5, which gives us x ≤ 6. Therefore, the solution set of 5x-9 ≤ 21 is x ≤ 6. This means that all values of x that are less than or equal to 6 make the inequality true.
How to Graph the Solution Set on a Number Line
In addition to finding the solution set of an inequality, it is also important to know how to graph the solution set on a number line. To do this, we need to identify the endpoint of the solution set. Since the solution set of 5x-9 ≤ 21 is x ≤ 6, the endpoint of the solution set is 6. We then need to draw a closed circle at 6 to indicate that 6 is included in the solution set. This indicates that all values of x that are less than or equal to 6 are in the solution set. Any values of x that are greater than 6 are not in the solution set. To make this more clear, we can also draw an arrow at 6 to indicate that the solution set does not include any values greater than 6.
Conclusion
In conclusion, the solution set of the inequality 5x-9 ≤ 21 is x ≤ 6. This means that all values of x that are less than or equal to 6 make the inequality true. To graph the solution set on a number line, we must identify the endpoint of the solution set, which is 6. We then need to draw a closed circle at 6 to indicate that 6 is included in the solution set and draw an arrow at 6 to indicate that the solution set does not include any values greater than 6.
The solution set of the inequality 5x-9 ≤ 21 is x ≤ 6. This means that all values of x that are less than or equal to 6 make the inequality true. To graph the solution set on a number line, we must identify the endpoint of the solution set, which is 6, and draw a closed circle at 6 to indicate that 6 is included in the solution set and draw an arrow at 6 to indicate that the solution set does not include any values greater than 6.
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