What Is The Solution Of The Equation $3x + 5 = 2x - 7$?A. The X-coordinate Of The Intersection Point Of The Lines $y = 3x + 5$ And $y = 2x - 7$.B. The X-coordinates Of The X-intercepts Of The Lines $y = 3x + 5$ And

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. When we encounter an equation like $3x + 5 = 2x - 7$, our goal is to isolate the variable $x$ and determine its value. In this article, we will explore the solution of the equation $3x + 5 = 2x - 7$ and understand the concept behind it.

Understanding the Equation

The given equation is a linear equation, which means it can be represented in the form of a straight line. The equation $3x + 5 = 2x - 7$ can be rewritten as $3x - 2x = -7 - 5$, which simplifies to $x = -12$. This means that the value of $x$ that satisfies the equation is $-12$.

The x-Coordinate of the Intersection Point

One of the options provided is that the solution is the x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$. To understand this, let's first find the intersection point of the two lines.

The equation $y = 3x + 5$ represents a line with a slope of $3$ and a y-intercept of $5$. Similarly, the equation $y = 2x - 7$ represents a line with a slope of $2$ and a y-intercept of $-7$.

To find the intersection point, we can set the two equations equal to each other and solve for $x$. This gives us:

$3x + 5 = 2x - 7$

Simplifying the equation, we get:

$x = -12$

This means that the x-coordinate of the intersection point of the two lines is indeed $-12$.

The x-Intercepts of the Lines

Another option provided is that the solution is the x-coordinates of the x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$. To understand this, let's first find the x-intercepts of the two lines.

The x-intercept of a line is the point where the line intersects the x-axis. This means that the y-coordinate of the x-intercept is always $0$.

For the line $y = 3x + 5$, we can set $y = 0$ and solve for $x$. This gives us:

$0 = 3x + 5$

Simplifying the equation, we get:

$x = -\frac{5}{3}$

This means that the x-intercept of the line $y = 3x + 5$ is $-\frac{5}{3}$.

Similarly, for the line $y = 2x - 7$, we can set $y = 0$ and solve for $x$. This gives us:

$0 = 2x - 7$

Simplifying the equation, we get:

$x = \frac{7}{2}$

This means that the x-intercept of the line $y = 2x - 7$ is $\frac{7}{2}$.

Conclusion

In conclusion, the solution of the equation $3x + 5 = 2x - 7$ is indeed the x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$, which is $-12$. Additionally, the x-coordinates of the x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$ are $-\frac{5}{3}$ and $\frac{7}{2}$, respectively.

Frequently Asked Questions

• What is the solution of the equation $3x + 5 = 2x - 7$? The solution of the equation $3x + 5 = 2x - 7$ is the x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$, which is $-12$.
• What are the x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$? The x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$ are $-\frac{5}{3}$ and $\frac{7}{2}$, respectively.

Final Thoughts

Solving equations is an essential concept in mathematics that helps us find the value of unknown variables. In this article, we explored the solution of the equation $3x + 5 = 2x - 7$ and understood the concept behind it. We also discussed the x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$, as well as the x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$.

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Introduction

In our previous article, we explored the solution of the equation $3x + 5 = 2x - 7$ and understood the concept behind it. We also discussed the x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$, as well as the x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$. In this article, we will answer some frequently asked questions about the equation $3x + 5 = 2x - 7$.

Q&A

Q: What is the solution of the equation $3x + 5 = 2x - 7$?

A: The solution of the equation $3x + 5 = 2x - 7$ is the x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$, which is $-12$.

Q: How do I solve the equation $3x + 5 = 2x - 7$?

A: To solve the equation $3x + 5 = 2x - 7$, you can follow these steps:

1. Subtract $2x$ from both sides of the equation to get $x + 5 = -7$.
2. Subtract $5$ from both sides of the equation to get $x = -12$.

Q: What is the x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$?

A: The x-coordinate of the intersection point of the lines $y = 3x + 5$ and $y = 2x - 7$ is $-12$.

Q: What are the x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$?

A: The x-intercepts of the lines $y = 3x + 5$ and $y = 2x - 7$ are $-\frac{5}{3}$ and $\frac{7}{2}$, respectively.

Q: How do I find the x-intercept of a line?

A: To find the x-intercept of a line, you can set $y = 0$ and solve for $x$. This will give you the x-coordinate of the x-intercept.

Q: What is the difference between the x-coordinate of the intersection point and the x-intercept of a line?

A: The x-coordinate of the intersection point of two lines is the value of $x$ that satisfies both equations. The x-intercept of a line is the point where the line intersects the x-axis.

Q: Can I use the equation $3x + 5 = 2x - 7$ to find the x-coordinate of the intersection point of two lines?

A: Yes, you can use the equation $3x + 5 = 2x - 7$ to find the x-coordinate of the intersection point of two lines. Simply solve the equation for $x$ and you will get the x-coordinate of the intersection point.

Conclusion

In conclusion, the equation $3x + 5 = 2x - 7$ is a simple linear equation that can be solved using basic algebraic techniques. We hope that this article has helped to clarify any questions you may have had about the equation and its solution. If you have any further questions, please don't hesitate to ask.

Final Thoughts

Solving equations is an essential concept in mathematics that helps us find the value of unknown variables. In this article, we answered some frequently asked questions about the equation $3x + 5 = 2x - 7$ and provided some tips and tricks for solving linear equations. We hope that this article has been helpful and informative.