Solve $3y + 4.6 = 5y$.Give Your Answer As A Decimal.

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Introduction

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to isolate the variable in a given equation. In this article, we will focus on solving the equation $3y + 4.6 = 5y$ and provide a step-by-step guide on how to arrive at the solution.

Understanding the Equation

The given equation is a linear equation in one variable, which means it has only one unknown value. The equation is $3y + 4.6 = 5y$, where $y$ is the variable we need to solve for. The equation has two terms on the left-hand side and one term on the right-hand side.

Isolating the Variable

To solve for $y$, we need to isolate the variable on one side of the equation. We can do this by subtracting $3y$ from both sides of the equation. This will give us:

$$4.6 = 5y - 3y$$

Simplifying the Equation

Now that we have isolated the variable, we can simplify the equation by combining like terms. In this case, we have $5y - 3y$, which simplifies to $2y$. So, the equation becomes:

$$4.6 = 2y$$

Solving for $y$

To solve for $y$, we need to isolate the variable by dividing both sides of the equation by $2$. This will give us:

$$y = \frac{4.6}{2}$$

Calculating the Value of $y$

Now that we have the equation $y = \frac{4.6}{2}$, we can calculate the value of $y$ by dividing $4.6$ by $2$. This gives us:

$$y = 2.3$$

Conclusion

In this article, we solved the equation $3y + 4.6 = 5y$ and arrived at the solution $y = 2.3$. We followed a step-by-step approach to isolate the variable and simplify the equation. By understanding how to solve linear equations, we can apply this knowledge to a wide range of mathematical problems.

Frequently Asked Questions

• What is the value of $y$ in the equation $3y + 4.6 = 5y$?
• How do I isolate the variable in a linear equation?
• What is the step-by-step process for solving a linear equation?

Answering the FAQs

• The value of $y$ in the equation $3y + 4.6 = 5y$ is $2.3$.
• To isolate the variable in a linear equation, you need to add or subtract the same value from both sides of the equation.
• The step-by-step process for solving a linear equation involves isolating the variable, simplifying the equation, and solving for the variable.

Real-World Applications

Solving linear equations has numerous real-world applications, including:

• Calculating the cost of goods and services
• Determining the amount of time it takes to complete a task
• Finding the area and perimeter of shapes
• Solving problems in physics and engineering

Tips and Tricks

• When solving linear equations, make sure to follow the order of operations (PEMDAS).
• Use a calculator to check your answers and ensure accuracy.
• Practice solving linear equations to build your confidence and skills.

Conclusion

Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to isolate the variable and simplify the equation, we can apply this knowledge to a wide range of mathematical problems. In this article, we solved the equation $3y + 4.6 = 5y$ and arrived at the solution $y = 2.3$. We hope this article has provided you with a better understanding of how to solve linear equations and has given you the confidence to tackle more complex mathematical problems.

Introduction

Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. In our previous article, we solved the equation $3y + 4.6 = 5y$ and arrived at the solution $y = 2.3$. In this article, we will answer some frequently asked questions about solving linear equations.

Q&A

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1, whereas a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: What is the step-by-step process for solving a linear equation?

A: The step-by-step process for solving a linear equation involves:

1. Isolating the variable by adding or subtracting the same value from both sides of the equation.
2. Simplifying the equation by combining like terms.
3. Solving for the variable by dividing both sides of the equation by the coefficient of the variable.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, you need to follow the same steps as solving a linear equation with fractions. You can also use a calculator to check your answers and ensure accuracy.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation with one variable, whereas a system of linear equations is a set of two or more equations with the same variables.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to use the method of substitution or elimination to find the values of the variables.

Q: What is the importance of solving linear equations in real-world applications?

A: Solving linear equations has numerous real-world applications, including calculating the cost of goods and services, determining the amount of time it takes to complete a task, finding the area and perimeter of shapes, and solving problems in physics and engineering.

Q: How do I check my answers when solving linear equations?

A: You can use a calculator to check your answers and ensure accuracy. You can also plug in the values of the variables into the original equation to see if it is true.

Tips and Tricks

• When solving linear equations, make sure to follow the order of operations (PEMDAS).
• Use a calculator to check your answers and ensure accuracy.
• Practice solving linear equations to build your confidence and skills.

Conclusion

Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to isolate the variable and simplify the equation, we can apply this knowledge to a wide range of mathematical problems. In this article, we answered some frequently asked questions about solving linear equations and provided tips and tricks for solving linear equations.

Frequently Asked Questions

• What is the difference between a linear equation and a quadratic equation?
• How do I solve a linear equation with fractions?
• What is the step-by-step process for solving a linear equation?
• How do I solve a linear equation with decimals?
• What is the difference between a linear equation and a system of linear equations?
• How do I solve a system of linear equations?
• What is the importance of solving linear equations in real-world applications?
• How do I check my answers when solving linear equations?

Answering the FAQs

• The difference between a linear equation and a quadratic equation is that a linear equation has the highest power of the variable as 1, whereas a quadratic equation has the highest power of the variable as 2.
• To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.
• The step-by-step process for solving a linear equation involves isolating the variable, simplifying the equation, and solving for the variable.
• To solve a linear equation with decimals, you need to follow the same steps as solving a linear equation with fractions.
• The difference between a linear equation and a system of linear equations is that a linear equation is a single equation with one variable, whereas a system of linear equations is a set of two or more equations with the same variables.
• To solve a system of linear equations, you need to use the method of substitution or elimination to find the values of the variables.
• The importance of solving linear equations in real-world applications is that it has numerous real-world applications, including calculating the cost of goods and services, determining the amount of time it takes to complete a task, finding the area and perimeter of shapes, and solving problems in physics and engineering.
• To check your answers when solving linear equations, you can use a calculator to check your answers and ensure accuracy, or plug in the values of the variables into the original equation to see if it is true.