Solved on Jan 17, 2024

Solve the linear equation $-8y - 8 = 6y + 6$ for the unknown variable $y$ .

STEP 1

Assumptions
1. The given equation is $-8y - 8 = 6y + 6$ .
2. We need to solve for the variable $y$ .

STEP 2

To solve for $y$ , we need to collect all terms containing $y$ on one side of the equation and the constant terms on the other side. We can do this by adding $8y$ to both sides of the equation to move the $y$ terms to the right side.
$-8y - 8 + 8y = 6y + 6 + 8y$

STEP 3

Now, simplify the equation by combining like terms on each side.
$-8 = 14y + 6$

STEP 4

Next, we need to isolate the $y$ terms by moving the constant term on the right side to the left side. We can do this by subtracting $6$ from both sides of the equation.
$-8 - 6 = 14y + 6 - 6$

STEP 5

Simplify the left side of the equation by combining the constants.
$-14 = 14y$

STEP 6

Now, we need to solve for $y$ by dividing both sides of the equation by the coefficient of $y$ , which is $14$ .
$\frac{-14}{14} = \frac{14y}{14}$

STEP 7

Simplify both sides of the equation to find the value of $y$ .
$y = -1$
The solution to the equation $-8y - 8 = 6y + 6$ is $y = -1$ .

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Solve the linear equation $-8y - 8 = 6y + 6$ for the unknown variable $y$ .

STEP 1

Assumptions
1. The given equation is $-8y - 8 = 6y + 6$ .
2. We need to solve for the variable $y$ .

STEP 2

To solve for $y$ , we need to collect all terms containing $y$ on one side of the equation and the constant terms on the other side. We can do this by adding $8y$ to both sides of the equation to move the $y$ terms to the right side.
$-8y - 8 + 8y = 6y + 6 + 8y$

STEP 3

Now, simplify the equation by combining like terms on each side.
$-8 = 14y + 6$

STEP 4

Next, we need to isolate the $y$ terms by moving the constant term on the right side to the left side. We can do this by subtracting $6$ from both sides of the equation.
$-8 - 6 = 14y + 6 - 6$

STEP 5

Simplify the left side of the equation by combining the constants.
$-14 = 14y$

STEP 6

Now, we need to solve for $y$ by dividing both sides of the equation by the coefficient of $y$ , which is $14$ .
$\frac{-14}{14} = \frac{14y}{14}$

STEP 7

Simplify both sides of the equation to find the value of $y$ .
$y = -1$
The solution to the equation $-8y - 8 = 6y + 6$ is $y = -1$ .

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Solve the linear equation −8y−8=6y+6-8y - 8 = 6y + 6−8y−8=6y+6 for the unknown variable yyy.

STEP 1

Assumptions1. The given equation is −8y−8=6y+6-8y - 8 = 6y + 6−8y−8=6y+6.2. We need to solve for the variable yyy.

STEP 2

STEP 3

Now, simplify the equation by combining like terms on each side.−8=14y+6-8 = 14y + 6−8=14y+6

STEP 4

Next, we need to isolate the yyy terms by moving the constant term on the right side to the left side. We can do this by subtracting 666 from both sides of the equation.−8−6=14y+6−6-8 - 6 = 14y + 6 - 6−8−6=14y+6−6

STEP 5

Simplify the left side of the equation by combining the constants.−14=14y-14 = 14y−14=14y

STEP 6

Now, we need to solve for yyy by dividing both sides of the equation by the coefficient of yyy, which is 141414.−1414=14y14\frac{-14}{14} = \frac{14y}{14}14−14​=1414y​

STEP 7

Simplify both sides of the equation to find the value of yyy.y=−1y = -1y=−1The solution to the equation −8y−8=6y+6-8y - 8 = 6y + 6−8y−8=6y+6 is y=−1y = -1y=−1.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the linear equation $-8y - 8 = 6y + 6$ for the unknown variable $y$ .

Assumptions
1. The given equation is $-8y - 8 = 6y + 6$ .
2. We need to solve for the variable $y$ .

Now, simplify the equation by combining like terms on each side.
$-8 = 14y + 6$

Next, we need to isolate the $y$ terms by moving the constant term on the right side to the left side. We can do this by subtracting $6$ from both sides of the equation.
$-8 - 6 = 14y + 6 - 6$

Simplify the left side of the equation by combining the constants.
$-14 = 14y$

Now, we need to solve for $y$ by dividing both sides of the equation by the coefficient of $y$ , which is $14$ .
$\frac{-14}{14} = \frac{14y}{14}$

Simplify both sides of the equation to find the value of $y$ .
$y = -1$
The solution to the equation $-8y - 8 = 6y + 6$ is $y = -1$ .