Solve For Y Y Y . − 2 5 Y + 1 2 = − 4 Y − 7 5 -\frac{2}{5} Y + \frac{1}{2} = -4y - \frac{7}{5} − 5 2 ​ Y + 2 1 ​ = − 4 Y − 5 7 ​

by ADMIN 129 views

===========================================================

Introduction

Solving for yy is a fundamental concept in algebra, and it's essential to understand how to isolate the variable in a linear equation. In this article, we'll explore the step-by-step process of solving for yy in the given equation: −25y+12=−4y−75-\frac{2}{5} y + \frac{1}{2} = -4y - \frac{7}{5}. We'll break down the solution into manageable steps, making it easy to follow and understand.

Understanding the Equation

Before we dive into solving for yy, let's take a closer look at the equation: −25y+12=−4y−75-\frac{2}{5} y + \frac{1}{2} = -4y - \frac{7}{5}. This equation is a linear equation, which means it can be written in the form ax+b=cx+dax + b = cx + d, where aa, bb, cc, and dd are constants.

Identifying the Variable

In this equation, the variable is yy. Our goal is to isolate yy on one side of the equation.

Simplifying the Equation

To simplify the equation, we can start by getting rid of the fractions. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 10.

10 \times \left(-\frac{2}{5} y + \frac{1}{2}\right) = 10 \times \left(-4y - \frac{7}{5}\right)

This simplifies the equation to:

-4y + 5 = -40y - 14

Isolating the Variable

Now that we have simplified the equation, we can start isolating the variable yy. We'll do this by getting rid of the terms that are not yy.

Adding 40y to Both Sides

To get rid of the −40y-40y term, we can add 40y40y to both sides of the equation.

-4y + 5 + 40y = -40y - 14 + 40y

This simplifies the equation to:

36y + 5 = -14

Subtracting 5 from Both Sides

Next, we'll subtract 5 from both sides of the equation to get rid of the constant term.

36y + 5 - 5 = -14 - 5

This simplifies the equation to:

36y = -19

Solving for yy

Now that we have isolated the variable yy, we can solve for yy by dividing both sides of the equation by 36.

\frac{36y}{36} = \frac{-19}{36}

This simplifies the equation to:

y = -\frac{19}{36}

Conclusion

Solving for yy is a straightforward process that involves simplifying the equation, isolating the variable, and solving for yy. By following the steps outlined in this article, you should be able to solve for yy in any linear equation. Remember to always simplify the equation, isolate the variable, and solve for yy by dividing both sides of the equation by the coefficient of the variable.

Final Answer

The final answer is −1936\boxed{-\frac{19}{36}}.

Related Topics

  • Solving linear equations
  • Isolating variables
  • Simplifying equations
  • Algebraic manipulations

References

===========================================================

Introduction

In our previous article, we explored the step-by-step process of solving for yy in the given equation: −25y+12=−4y−75-\frac{2}{5} y + \frac{1}{2} = -4y - \frac{7}{5}. We broke down the solution into manageable steps, making it easy to follow and understand. In this article, we'll answer some of the most frequently asked questions about solving for yy.

Q&A

Q: What is the first step in solving for yy?

A: The first step in solving for yy is to simplify the equation by getting rid of the fractions. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: How do I simplify the equation?

A: To simplify the equation, we can start by identifying the fractions and multiplying both sides of the equation by the LCM of the denominators. For example, if the equation is −25y+12=−4y−75-\frac{2}{5} y + \frac{1}{2} = -4y - \frac{7}{5}, we can multiply both sides by 10 to get rid of the fractions.

Q: What is the next step in solving for yy?

A: After simplifying the equation, the next step is to isolate the variable yy. We can do this by getting rid of the terms that are not yy.

Q: How do I isolate the variable yy?

A: To isolate the variable yy, we can add or subtract the same value to both sides of the equation. For example, if the equation is 36y+5=−1436y + 5 = -14, we can subtract 5 from both sides to get rid of the constant term.

Q: What is the final step in solving for yy?

A: The final step in solving for yy is to solve for yy by dividing both sides of the equation by the coefficient of the variable.

Q: How do I solve for yy?

A: To solve for yy, we can divide both sides of the equation by the coefficient of the variable. For example, if the equation is 36y=−1936y = -19, we can divide both sides by 36 to get y=−1936y = -\frac{19}{36}.

Common Mistakes

Mistake 1: Not simplifying the equation

A: Failing to simplify the equation can make it difficult to isolate the variable yy. Make sure to simplify the equation by getting rid of the fractions.

Mistake 2: Not isolating the variable yy

A: Failing to isolate the variable yy can make it difficult to solve for yy. Make sure to isolate the variable yy by getting rid of the terms that are not yy.

Mistake 3: Not solving for yy

A: Failing to solve for yy can make it difficult to find the value of yy. Make sure to solve for yy by dividing both sides of the equation by the coefficient of the variable.

Conclusion

Solving for yy is a straightforward process that involves simplifying the equation, isolating the variable, and solving for yy. By following the steps outlined in this article, you should be able to solve for yy in any linear equation. Remember to always simplify the equation, isolate the variable, and solve for yy by dividing both sides of the equation by the coefficient of the variable.

Final Tips

  • Make sure to simplify the equation by getting rid of the fractions.
  • Isolate the variable yy by getting rid of the terms that are not yy.
  • Solve for yy by dividing both sides of the equation by the coefficient of the variable.

Related Topics

  • Solving linear equations
  • Isolating variables
  • Simplifying equations
  • Algebraic manipulations

References