What Is The Solution To This Equation? 3 X − 5 + 2 X = 25 3x - 5 + 2x = 25 3 X − 5 + 2 X = 25 A. X = 6 X = 6 X = 6 B. X = 4 X = 4 X = 4 C. X = 20 X = 20 X = 20 D. X = 30 X = 30 X = 30

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Introduction

Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various fields such as science, engineering, economics, and finance. In mathematics, equations are used to represent relationships between variables. Solving equations is an essential skill in mathematics, and it is used to find the value of unknown variables.

In this article, we will discuss the solution to the equation $3x - 5 + 2x = 25$. This equation is a linear equation, and it can be solved using basic algebraic techniques.

Understanding the Equation

The given equation is $3x - 5 + 2x = 25$. This equation can be simplified by combining like terms. The like terms in this equation are $3x$ and $2x$, which can be combined to form $5x$. The equation can be rewritten as $5x - 5 = 25$.

Solving the Equation

To solve the equation $5x - 5 = 25$, we need to isolate the variable $x$. We can do this by adding $5$ to both sides of the equation. This will give us $5x = 30$.

Isolating the Variable

Now that we have $5x = 30$, we can isolate the variable $x$ by dividing both sides of the equation by $5$. This will give us $x = 6$.

Conclusion

In conclusion, the solution to the equation $3x - 5 + 2x = 25$ is $x = 6$. This is the value of the variable $x$ that satisfies the equation.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Simplify the equation by combining like terms: $3x - 5 + 2x = 25$ becomes $5x - 5 = 25$.
2. Add $5$ to both sides of the equation: $5x - 5 + 5 = 25 + 5$.
3. Simplify the equation: $5x = 30$.
4. Divide both sides of the equation by $5$: $x = 30/5$.
5. Simplify the equation: $x = 6$.

Final Answer

The final answer to the equation $3x - 5 + 2x = 25$ is $x = 6$.

Comparison with Other Options

Let's compare the solution $x = 6$ with the other options:

• Option A: $x = 6$
• Option B: $x = 4$
• Option C: $x = 20$
• Option D: $x = 30$

As we can see, the solution $x = 6$ is the only option that satisfies the equation.

Importance of Solving Equations

Solving equations is an essential skill in mathematics. It is used in various fields such as science, engineering, economics, and finance. Solving equations helps us to understand the relationships between variables and to make predictions about the behavior of systems.

Real-World Applications

Solving equations has many real-world applications. For example, in physics, equations are used to describe the motion of objects. In economics, equations are used to model the behavior of markets. In finance, equations are used to calculate interest rates and investment returns.

Conclusion

In conclusion, the solution to the equation $3x - 5 + 2x = 25$ is $x = 6$. Solving equations is an essential skill in mathematics, and it has many real-world applications.

Introduction

Solving equations is a fundamental concept in mathematics that has many real-world applications. In our previous article, we discussed the solution to the equation $3x - 5 + 2x = 25$. In this article, we will answer some frequently asked questions (FAQs) about solving equations.

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions. It is a fundamental concept in mathematics that is used to represent relationships between variables.

Q: What is a variable?

A: A variable is a symbol or a letter that represents a value that can change. In an equation, variables are used to represent unknown values.

Q: What is a constant?

A: A constant is a value that does not change. In an equation, constants are used to represent fixed values.

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable by performing operations on both sides of the equation. This can involve adding, subtracting, multiplying, or dividing both sides of the equation.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate exponents next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate addition and subtraction operations from left to right.

Q: How do I simplify an equation?

A: To simplify an equation, you need to combine like terms and eliminate any unnecessary operations. This can involve combining constants, combining variables, or eliminating parentheses.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be solved using basic algebraic techniques.

Q: What is a quadratic equation?

A: A quadratic equation is an equation in which the highest power of the variable is 2. Quadratic equations can be solved using the quadratic formula or factoring.

Q: How do I use the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: What is the quadratic formula used for?

A: The quadratic formula is used to solve quadratic equations that cannot be factored. It is a powerful tool that can be used to solve a wide range of quadratic equations.

Q: How do I graph an equation?

A: To graph an equation, you need to plot points on a coordinate plane and connect them to form a line or a curve. This can be done using a graphing calculator or by hand.

Q: What is the importance of graphing equations?

A: Graphing equations is an important skill in mathematics that has many real-world applications. It is used to visualize data, to model real-world situations, and to make predictions about the behavior of systems.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics that has many real-world applications. In this article, we answered some frequently asked questions (FAQs) about solving equations. We hope that this article has been helpful in providing you with a better understanding of solving equations.

Additional Resources

If you are interested in learning more about solving equations, we recommend the following resources:

• Khan Academy: Solving Equations
• Mathway: Solving Equations
• Wolfram Alpha: Solving Equations

Final Thoughts

Solving equations is a skill that is used in many real-world applications. It is an important concept in mathematics that has many practical uses. We hope that this article has been helpful in providing you with a better understanding of solving equations.