6 ( 9 Y − 1 ) − 10 ( 5 Y ) − 3 Y = 22 − 4 ( 2 Y − 12 ) + 8 ( Y − 6 )
Introduction
In this article, we will be solving a complex algebraic equation involving multiple variables and operations. The given equation is 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 − 4 ( 2 y − 12 ) + 8 ( y − 6 ). Our goal is to simplify this equation and find the value of the variable 'y'.
Step 1: Distribute the coefficients to the terms inside the parentheses
To simplify the equation, we need to distribute the coefficients to the terms inside the parentheses. This will help us to combine like terms and simplify the equation.
6(9y - 1) = 54y - 6
-10(5y) = -50y
-3y = -3y
22 = 22
-4(2y - 12) = -8y + 48
8(y - 6) = 8y - 48
Step 2: Combine like terms
Now that we have distributed the coefficients to the terms inside the parentheses, we can combine like terms to simplify the equation.
54y - 6 - 50y - 3y = -22 + 8y - 48 + 8y
Step 3: Simplify the equation
Let's simplify the equation by combining like terms.
54y - 50y - 3y = -22 + 8y + 8y - 48
Step 4: Combine like terms
Now that we have simplified the equation, we can combine like terms to get the final result.
y = -22 + 16y - 48
Step 5: Isolate the variable 'y'
To isolate the variable 'y', we need to move all the terms involving 'y' to one side of the equation and the constant terms to the other side.
y - 16y = -22 - 48
Step 6: Combine like terms
Now that we have isolated the variable 'y', we can combine like terms to get the final result.
-15y = -70
Step 7: Solve for 'y'
To solve for 'y', we need to divide both sides of the equation by -15.
y = -70 / -15
y = 4.67
Conclusion
In this article, we have solved a complex algebraic equation involving multiple variables and operations. We have distributed the coefficients to the terms inside the parentheses, combined like terms, simplified the equation, isolated the variable 'y', and finally solved for 'y'. The value of the variable 'y' is 4.67.
Final Answer
The final answer is .
Introduction
In our previous article, we solved a complex algebraic equation involving multiple variables and operations. The given equation was 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 − 4 ( 2 y − 12 ) + 8 ( y − 6 ). We distributed the coefficients to the terms inside the parentheses, combined like terms, simplified the equation, isolated the variable 'y', and finally solved for 'y'. The value of the variable 'y' is 4.67. In this article, we will answer some frequently asked questions related to the solution of the equation.
Q&A
Q1: What is the first step in solving the equation 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 − 4 ( 2 y − 12 ) + 8 ( y − 6 )?
A1: The first step in solving the equation is to distribute the coefficients to the terms inside the parentheses.
Q2: How do we combine like terms in the equation?
A2: We combine like terms by grouping the terms with the same variable and coefficient.
Q3: What is the value of the variable 'y' in the equation?
A3: The value of the variable 'y' in the equation is 4.67.
Q4: How do we isolate the variable 'y' in the equation?
A4: We isolate the variable 'y' by moving all the terms involving 'y' to one side of the equation and the constant terms to the other side.
Q5: What is the final answer to the equation 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 − 4 ( 2 y − 12 ) + 8 ( y − 6 )?
A5: The final answer to the equation is .
Q6: What is the purpose of distributing the coefficients to the terms inside the parentheses?
A6: The purpose of distributing the coefficients to the terms inside the parentheses is to simplify the equation and make it easier to solve.
Q7: How do we simplify the equation 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 − 4 ( 2 y − 12 ) + 8 ( y − 6 )?
A7: We simplify the equation by combining like terms and isolating the variable 'y'.
Q8: What is the importance of combining like terms in the equation?
A8: The importance of combining like terms in the equation is to simplify the equation and make it easier to solve.
Q9: How do we check the solution of the equation?
A9: We check the solution of the equation by plugging the value of the variable 'y' back into the original equation and verifying that it is true.
Q10: What is the final step in solving the equation 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 − 4 ( 2 y − 12 ) + 8 ( y − 6 )?
A10: The final step in solving the equation is to check the solution by plugging the value of the variable 'y' back into the original equation and verifying that it is true.
Conclusion
In this article, we have answered some frequently asked questions related to the solution of the equation 6 ( 9 y − 1 ) − 10 ( 5 y ) − 3 y = 22 − 4 ( 2 y − 12 ) + 8 ( y − 6 ). We have discussed the importance of distributing the coefficients to the terms inside the parentheses, combining like terms, isolating the variable 'y', and checking the solution. The value of the variable 'y' is 4.67.
Final Answer
The final answer is .