Graph The Solution Of This Inequality:${ 350 \geq 125 + 15x }$Drag A Point To The Number Line To Represent The Solution.
Introduction
In mathematics, inequalities are used to compare two or more values. They are an essential part of algebra and are used to solve a wide range of problems. In this article, we will focus on graphing the solution of the inequality 350 ≥ 125 + 15x. We will use a number line to represent the solution and explore the different ways to solve this type of inequality.
Understanding the Inequality
The given inequality is 350 ≥ 125 + 15x. To solve this inequality, we need to isolate the variable x. We can start by subtracting 125 from both sides of the inequality. This gives us 225 ≥ 15x.
Isolating the Variable
Next, we need to isolate the variable x. We can do this by dividing both sides of the inequality by 15. This gives us x ≤ 15.
Graphing the Solution
To graph the solution of the inequality, we need to use a number line. A number line is a line that has numbers marked at equal intervals. We can use a number line to represent the solution of the inequality by marking a point on the line that represents the value of x.
Using a Number Line to Represent the Solution
To use a number line to represent the solution of the inequality, we need to mark a point on the line that represents the value of x. We can do this by finding the midpoint of the number line and marking a point at that location. The midpoint of the number line is the value of x that satisfies the inequality.
Finding the Midpoint
To find the midpoint of the number line, we need to divide the length of the number line by 2. In this case, the length of the number line is 15 units. Therefore, the midpoint is 7.5 units from the origin.
Marking the Point on the Number Line
Once we have found the midpoint, we can mark a point on the number line at that location. This point represents the value of x that satisfies the inequality.
Understanding the Solution
The solution of the inequality is all values of x that are less than or equal to 15. This means that any value of x that is less than or equal to 15 will satisfy the inequality.
Graphing the Solution on a Number Line
To graph the solution of the inequality on a number line, we need to mark a point on the line that represents the value of x. We can do this by finding the midpoint of the number line and marking a point at that location.
Using a Number Line to Graph the Solution
A number line is a line that has numbers marked at equal intervals. We can use a number line to graph the solution of the inequality by marking a point on the line that represents the value of x.
Graphing the Solution of the Inequality
To graph the solution of the inequality, we need to use a number line. We can mark a point on the line that represents the value of x. The point should be marked at the location that represents the value of x that satisfies the inequality.
Conclusion
In conclusion, graphing the solution of the inequality 350 ≥ 125 + 15x involves using a number line to represent the solution. We can mark a point on the line that represents the value of x that satisfies the inequality. The solution of the inequality is all values of x that are less than or equal to 15.
Frequently Asked Questions
- What is the solution of the inequality 350 ≥ 125 + 15x? The solution of the inequality is all values of x that are less than or equal to 15.
- How do I graph the solution of the inequality on a number line? To graph the solution of the inequality on a number line, you need to mark a point on the line that represents the value of x. You can do this by finding the midpoint of the number line and marking a point at that location.
- What is the midpoint of the number line? The midpoint of the number line is the value of x that satisfies the inequality. In this case, the midpoint is 7.5 units from the origin.
Step-by-Step Solution
- Subtract 125 from both sides of the inequality: 350 ≥ 125 + 15x becomes 225 ≥ 15x.
- Divide both sides of the inequality by 15: x ≤ 15.
- Graph the solution on a number line: Mark a point on the line that represents the value of x. The point should be marked at the location that represents the value of x that satisfies the inequality.
Final Answer
The final answer is x ≤ 15.
Introduction
In the previous article, we discussed how to graph the solution of the inequality 350 ≥ 125 + 15x. We used a number line to represent the solution and found that the solution is all values of x that are less than or equal to 15. In this article, we will answer some frequently asked questions about graphing the solution of the inequality.
Q&A
Q: What is the solution of the inequality 350 ≥ 125 + 15x?
A: The solution of the inequality is all values of x that are less than or equal to 15.
Q: How do I graph the solution of the inequality on a number line?
A: To graph the solution of the inequality on a number line, you need to mark a point on the line that represents the value of x. You can do this by finding the midpoint of the number line and marking a point at that location.
Q: What is the midpoint of the number line?
A: The midpoint of the number line is the value of x that satisfies the inequality. In this case, the midpoint is 7.5 units from the origin.
Q: How do I find the midpoint of the number line?
A: To find the midpoint of the number line, you need to divide the length of the number line by 2. In this case, the length of the number line is 15 units, so the midpoint is 7.5 units from the origin.
Q: What if the inequality is not in the form x ≤ 15?
A: If the inequality is not in the form x ≤ 15, you need to isolate the variable x by performing the necessary operations. For example, if the inequality is 350 ≥ 125 + 3x, you need to divide both sides by 3 to get x ≤ 25.
Q: Can I use a graphing calculator to graph the solution of the inequality?
A: Yes, you can use a graphing calculator to graph the solution of the inequality. However, it's always a good idea to check your work by graphing the solution on a number line.
Q: What if I make a mistake when graphing the solution of the inequality?
A: If you make a mistake when graphing the solution of the inequality, don't worry! Just go back and recheck your work. Make sure you have isolated the variable x correctly and that you have marked the correct point on the number line.
Q: Can I graph the solution of the inequality on a coordinate plane?
A: Yes, you can graph the solution of the inequality on a coordinate plane. However, it's always a good idea to use a number line to represent the solution, especially if you're not familiar with graphing on a coordinate plane.
Conclusion
Graphing the solution of the inequality 350 ≥ 125 + 15x involves using a number line to represent the solution. We can mark a point on the line that represents the value of x that satisfies the inequality. The solution of the inequality is all values of x that are less than or equal to 15. We hope this article has helped you understand how to graph the solution of the inequality and answer some frequently asked questions.
Step-by-Step Solution
- Subtract 125 from both sides of the inequality: 350 ≥ 125 + 15x becomes 225 ≥ 15x.
- Divide both sides of the inequality by 15: x ≤ 15.
- Graph the solution on a number line: Mark a point on the line that represents the value of x. The point should be marked at the location that represents the value of x that satisfies the inequality.
Final Answer
The final answer is x ≤ 15.