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Which Graph Shows the Solution of 9-C 2 Or-3 C15?

In mathematics, graphs are a visual representation of data and relationships between different variables. They are used to present information in a clear and concise manner, making it easier for us to understand complex concepts. When it comes to solving equations, graphs can be particularly useful in illustrating the solutions.

In this article, we will explore the equation 9-C 2 Or-3 C15 and analyze which graph represents its solution. We will also provide a comprehensive FAQ section to address common queries regarding this equation.

Understanding the Equation 9-C 2 Or-3 C15:

The given equation, 9-C 2 Or-3 C15, may seem a bit unfamiliar at first glance. However, we can break it down to understand its components.

The expression “9-C” represents the difference between 9 and C. This means that we subtract the value of C from 9.

On the other hand, “2 Or-3 C15” is a more complex expression. The term “2 Or” implies that we have two different possibilities for the equation. The “3 C15” is a product of 3 and C15.

Considering these components, the equation can be rewritten as 9-C = 2 or 9-C = -3 C15.

Analyzing the Solutions:

To determine which graph represents the solution of this equation, we need to solve it first. Let’s solve each possibility separately and observe the resulting graphs.

1. Solving 9-C = 2:

To solve this equation, we aim to find the value of C that satisfies the equation. By subtracting 9 from both sides, we get -C = -7. Multiplying both sides by -1, we find that C = 7.

Now, let’s plot this solution on a graph. We represent the value of C on the x-axis and the value of the equation (9-C) on the y-axis. The graph will have a single point at (7, 2), indicating that C = 7 satisfies the equation.

2. Solving 9-C = -3 C15:

To solve this equation, we need to simplify it. By expanding -3 C15, we obtain -3C^15. Now, let’s bring all terms to one side to form a quadratic equation. Rearranging the equation, we have 3C^15 – C – 9 = 0.

Solving this quadratic equation may require advanced mathematical techniques such as factoring, completing the square, or using the quadratic formula. The resulting values of C will be the solutions to this equation.

Once we have the solutions, we can plot them on a graph similar to the previous case. Each solution will be represented by a point on the graph.

FAQs:

Q: How can I determine the solution of 9-C 2 Or-3 C15 without a graph?

A: To determine the solution without a graph, you can solve the equation algebraically. By isolating the variable C and simplifying the equation, you can find the solutions.

Q: Are there any other methods to solve the equation 9-C 2 Or-3 C15?

A: Yes, there are various methods to solve equations, such as factoring, completing the square, or using the quadratic formula. The choice of method depends on the complexity of the equation and your familiarity with the techniques.

Q: Can you provide an example of a quadratic equation similar to 9-C 2 Or-3 C15?

A: Certainly! A similar quadratic equation could be 2x^2 + 5x – 3 = 0. By applying the quadratic formula or factoring, you can find the solutions for this equation.

Q: How can I verify if my solution to the equation is correct?

A: You can substitute the value of C back into the original equation and check if it satisfies the equation. If the equation holds true, your solution is correct.

Conclusion:

In conclusion, the equation 9-C 2 Or-3 C15 can be solved algebraically to determine its solutions. By plotting the solutions on a graph, we can visually represent the solutions. Remember that the graph for each possibility will consist of points that satisfy the equation. Understanding how to interpret and analyze graphs can greatly assist in solving equations and understanding their solutions.

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