Solve For Y Y Y .${4(y-5)-2=-4(-5y+8)-y} S I M P L I F Y Y O U R A N S W E R A S M U C H A S P O S S I B L E . Simplify Your Answer As Much As Possible. S Im Pl I F Yyo U R An S W Er A S M U C Ha S P Oss Ib L E . {y=\}

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Introduction

Solving for $y$ in a linear equation is a fundamental concept in algebra. It involves isolating the variable $y$ on one side of the equation, while the constants are on the other side. In this article, we will simplify the given equation and solve for $y$. We will use algebraic techniques to manipulate the equation and isolate the variable.

The Given Equation

The given equation is:

${4(y-5)-2=-4(-5y+8)-y}$

Our goal is to simplify this equation and solve for $y$.

Step 1: Distribute the Numbers

To simplify the equation, we need to distribute the numbers inside the parentheses. We will start by distributing the 4 to the terms inside the first set of parentheses:

${4(y-5)-2=-4(-5y+8)-y}$

${4y-20-2=-4(-5y+8)-y}$

Step 2: Simplify the Left Side

Now, we will simplify the left side of the equation by combining the constants:

${4y-22=-4(-5y+8)-y}$

Step 3: Distribute the Negative 4

Next, we will distribute the negative 4 to the terms inside the second set of parentheses:

${4y-22=20y-32-y}$

Step 4: Combine Like Terms

Now, we will combine the like terms on the right side of the equation:

${4y-22=19y-32}$

Step 5: Add 22 to Both Sides

To isolate the variable $y$, we need to get rid of the constant term on the left side. We will add 22 to both sides of the equation:

${4y-22+22=19y-32+22}$

${4y=19y-10}$

Step 6: Subtract 19y from Both Sides

Now, we will subtract 19y from both sides of the equation to isolate the variable $y$:

${4y-19y=19y-19y-10}$

${-15y=-10}$

Step 7: Divide Both Sides by -15

Finally, we will divide both sides of the equation by -15 to solve for $y$:

${\frac{-15y}{-15}=\frac{-10}{-15}}$

${y=\frac{2}{3}}$

Conclusion

In this article, we simplified the given equation and solved for $y$. We used algebraic techniques to manipulate the equation and isolate the variable. The final solution is $y=\frac{2}{3}$. This is the value of $y$ that satisfies the given equation.

Tips and Tricks

• When solving for $y$, it's essential to isolate the variable on one side of the equation.
• Use algebraic techniques such as distributing numbers, combining like terms, and adding or subtracting constants to simplify the equation.
• Be careful when dividing both sides of the equation by a negative number, as it will change the sign of the variable.

Frequently Asked Questions

• Q: What is the value of $y$ in the given equation? A: The value of $y$ is $\frac{2}{3}$.
• Q: How do I simplify the equation and solve for $y$? A: Use algebraic techniques such as distributing numbers, combining like terms, and adding or subtracting constants to simplify the equation.
• Q: What if the equation has multiple variables? A: In that case, you will need to use more advanced algebraic techniques such as substitution or elimination to solve for the variables.

See Also

• Solving Linear Equations
• Algebraic Techniques
• Isolating Variables

References

• [1] Algebra: A Comprehensive Introduction
• [2] Linear Equations: A Guide to Solving
• [3] Algebraic Techniques: A Handbook for Students
  

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Introduction

In our previous article, we simplified the given equation and solved for $y$. However, we understand that some readers may still have questions or need further clarification on the topic. In this article, we will address some of the most frequently asked questions related to solving for $y$.

Q&A

Q: What is the value of $y$ in the given equation?

A: The value of $y$ is $\frac{2}{3}$.

Q: How do I simplify the equation and solve for $y$?

A: To simplify the equation and solve for $y$, you can use algebraic techniques such as distributing numbers, combining like terms, and adding or subtracting constants. Start by distributing the numbers inside the parentheses, then combine like terms and isolate the variable $y$.

Q: What if the equation has multiple variables?

A: If the equation has multiple variables, you will need to use more advanced algebraic techniques such as substitution or elimination to solve for the variables. For example, you can substitute one variable in terms of the other variable, or use the elimination method to eliminate one variable and solve for the other.

Q: How do I know which algebraic technique to use?

A: The choice of algebraic technique depends on the specific equation and the variables involved. For example, if the equation has a variable in the numerator and a constant in the denominator, you may need to use the substitution method. On the other hand, if the equation has multiple variables and you need to eliminate one variable, you may need to use the elimination method.

Q: What if I get stuck or make a mistake?

A: Don't worry if you get stuck or make a mistake! It's a normal part of the learning process. Take a step back, review the equation and the steps you've taken, and try to identify where you went wrong. If you're still stuck, try asking a teacher or tutor for help.

Q: Can I use a calculator to solve for $y$?

A: While calculators can be a useful tool for solving equations, it's generally not recommended to rely solely on a calculator to solve for $y$. Instead, try to use algebraic techniques to simplify the equation and solve for $y$. This will help you develop a deeper understanding of the material and improve your problem-solving skills.

Q: How do I check my answer?

A: To check your answer, plug the value of $y$ back into the original equation and see if it's true. If the equation holds true, then your answer is correct. If not, then you may need to re-evaluate your solution.

Tips and Tricks

• Always read the problem carefully and understand what's being asked.
• Use algebraic techniques such as distributing numbers, combining like terms, and adding or subtracting constants to simplify the equation.
• Be careful when dividing both sides of the equation by a negative number, as it will change the sign of the variable.
• Don't be afraid to ask for help if you're stuck or make a mistake.

See Also

• Solving Linear Equations
• Algebraic Techniques
• Isolating Variables

References

• [1] Algebra: A Comprehensive Introduction
• [2] Linear Equations: A Guide to Solving
• [3] Algebraic Techniques: A Handbook for Students

Additional Resources

• Online algebra tutorials and resources
• Algebra textbooks and workbooks
• Online communities and forums for algebra enthusiasts

Conclusion

Solving for $y$ is an essential skill in algebra, and with practice and patience, you can master it. Remember to use algebraic techniques such as distributing numbers, combining like terms, and adding or subtracting constants to simplify the equation. Don't be afraid to ask for help if you're stuck or make a mistake, and always check your answer to ensure it's correct. With these tips and tricks, you'll be well on your way to becoming an algebra expert!