Select The Correct Answer.Which Equation Is Correctly Rewritten To Solve For $y$?$12y + D = -19y + T$A. \$y = \frac{t + D}{-7}$[/tex\] B. $y = \frac{t - D}{31}$ C. $y = 31(t - D)$ D.
Introduction
In algebra, solving for a variable in an equation is a fundamental concept. It involves isolating the variable on one side of the equation, while the other side remains constant. In this article, we will focus on solving for y in a linear equation, specifically the equation 12y + d = -19y + t. We will examine each option and determine which one is the correct solution.
The Original Equation
The original equation is 12y + d = -19y + t. To solve for y, we need to isolate y on one side of the equation. We can start by adding 19y to both sides of the equation to get all the y terms on one side.
12y + d = -19y + t
12y + 19y + d = -19y + 19y + t
31y + d = t
Option A: y = (t + d) / -7
Option A is y = (t + d) / -7. To determine if this is the correct solution, we need to compare it to the original equation. We can start by multiplying both sides of the equation by -7 to get rid of the fraction.
y = (t + d) / -7
-7y = t + d
Now, we can compare this to the original equation. We can see that the left side of the equation is -7y, which is equivalent to the left side of the original equation. However, the right side of the equation is t + d, which is not equivalent to the right side of the original equation.
Option B: y = (t - d) / 31
Option B is y = (t - d) / 31. To determine if this is the correct solution, we need to compare it to the original equation. We can start by multiplying both sides of the equation by 31 to get rid of the fraction.
y = (t - d) / 31
31y = t - d
Now, we can compare this to the original equation. We can see that the left side of the equation is 31y, which is equivalent to the left side of the original equation. However, the right side of the equation is t - d, which is not equivalent to the right side of the original equation.
Option C: y = 31(t - d)
Option C is y = 31(t - d). To determine if this is the correct solution, we need to compare it to the original equation. We can start by multiplying both sides of the equation by 31 to get rid of the fraction.
y = 31(t - d)
31y = 31(t - d)
Now, we can compare this to the original equation. We can see that the left side of the equation is 31y, which is equivalent to the left side of the original equation. However, the right side of the equation is 31(t - d), which is not equivalent to the right side of the original equation.
Conclusion
In conclusion, none of the options A, B, or C are the correct solution to the equation 12y + d = -19y + t. The correct solution is y = (t - d) / 31, which is not among the options. This is because the correct solution involves isolating y on one side of the equation, while the other side remains constant.
Final Answer
Introduction
In our previous article, we discussed how to solve for y in a linear equation, specifically the equation 12y + d = -19y + t. We examined each option and determined that none of them were the correct solution. In this article, we will provide a Q&A section to help clarify any confusion and provide additional information on solving for y in a linear equation.
Q: What is the correct solution to the equation 12y + d = -19y + t?
A: The correct solution to the equation 12y + d = -19y + t is y = (t - d) / 31.
Q: Why is the correct solution y = (t - d) / 31?
A: The correct solution y = (t - d) / 31 is because we need to isolate y on one side of the equation, while the other side remains constant. To do this, we can add 19y to both sides of the equation to get all the y terms on one side. This gives us 31y + d = t. We can then divide both sides of the equation by 31 to get y = (t - d) / 31.
Q: How do I know which side of the equation to isolate y on?
A: To determine which side of the equation to isolate y on, we need to look at the equation and determine which side has the variable y. In this case, the variable y is on the left side of the equation, so we need to isolate y on the left side.
Q: What if the equation has multiple variables?
A: If the equation has multiple variables, we need to isolate one variable on one side of the equation, while the other variables remain on the other side. We can do this by using the same steps as before, adding or subtracting the same value to both sides of the equation to get all the variables on one side.
Q: Can I use a calculator to solve for y?
A: Yes, you can use a calculator to solve for y. However, it's always a good idea to check your work by plugging the solution back into the original equation to make sure it's true.
Q: What if I get a negative solution for y?
A: If you get a negative solution for y, it means that the value of y is less than 0. This is okay, as long as the solution is consistent with the original equation.
Q: Can I use this method to solve for other variables?
A: Yes, you can use this method to solve for other variables. The steps are the same, regardless of which variable you're solving for.
Conclusion
In conclusion, solving for y in a linear equation involves isolating y on one side of the equation, while the other side remains constant. We can do this by adding or subtracting the same value to both sides of the equation to get all the y terms on one side. The correct solution to the equation 12y + d = -19y + t is y = (t - d) / 31. We hope this Q&A section has helped clarify any confusion and provided additional information on solving for y in a linear equation.
Final Answer
The final answer is y = (t - d) / 31.