Solved on Feb 29, 2024

Solve the linear equation $-y-8 \frac{2}{7}=0$ for the unknown variable $y$ .

STEP 1

Assumptions
1. The equation to solve is $-y - 8\frac{2}{7} = 0$ .
2. We need to isolate $y$ to find its value.

STEP 2

First, we need to convert the mixed number $8\frac{2}{7}$ to an improper fraction to make the calculation easier.
$8\frac{2}{7} = 8 + \frac{2}{7}$

STEP 3

To convert the mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.
$8\frac{2}{7} = \frac{8 \times 7}{7} + \frac{2}{7}$

STEP 4

Complete the multiplication and addition to find the improper fraction.
$8\frac{2}{7} = \frac{56}{7} + \frac{2}{7} = \frac{58}{7}$

STEP 5

Now that we have the mixed number as an improper fraction, we can rewrite the equation.
$-y - \frac{58}{7} = 0$

STEP 6

To isolate $y$ , we need to add $\frac{58}{7}$ to both sides of the equation.
$-y - \frac{58}{7} + \frac{58}{7} = 0 + \frac{58}{7}$

STEP 7

Simplify both sides of the equation.
$-y = \frac{58}{7}$

STEP 8

To find the value of $y$ , we need to multiply both sides of the equation by $-1$ to get a positive $y$ .
$-1 \times (-y) = -1 \times \frac{58}{7}$

STEP 9

Simplify both sides of the equation to find the value of $y$ .
$y = -\frac{58}{7}$

STEP 10

The value of $y$ is $-\frac{58}{7}$ , which can also be written as a mixed number.
$y = -8\frac{2}{7}$
Therefore, the solution to the equation $-y - 8\frac{2}{7} = 0$ is $y = -8\frac{2}{7}$ .

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Solve the linear equation $-y-8 \frac{2}{7}=0$ for the unknown variable $y$ .

STEP 1

Assumptions
1. The equation to solve is $-y - 8\frac{2}{7} = 0$ .
2. We need to isolate $y$ to find its value.

STEP 2

First, we need to convert the mixed number $8\frac{2}{7}$ to an improper fraction to make the calculation easier.
$8\frac{2}{7} = 8 + \frac{2}{7}$

STEP 3

To convert the mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.
$8\frac{2}{7} = \frac{8 \times 7}{7} + \frac{2}{7}$

STEP 4

Complete the multiplication and addition to find the improper fraction.
$8\frac{2}{7} = \frac{56}{7} + \frac{2}{7} = \frac{58}{7}$

STEP 5

Now that we have the mixed number as an improper fraction, we can rewrite the equation.
$-y - \frac{58}{7} = 0$

STEP 6

To isolate $y$ , we need to add $\frac{58}{7}$ to both sides of the equation.
$-y - \frac{58}{7} + \frac{58}{7} = 0 + \frac{58}{7}$

STEP 7

Simplify both sides of the equation.
$-y = \frac{58}{7}$

STEP 8

To find the value of $y$ , we need to multiply both sides of the equation by $-1$ to get a positive $y$ .
$-1 \times (-y) = -1 \times \frac{58}{7}$

STEP 9

Simplify both sides of the equation to find the value of $y$ .
$y = -\frac{58}{7}$

STEP 10

The value of $y$ is $-\frac{58}{7}$ , which can also be written as a mixed number.
$y = -8\frac{2}{7}$
Therefore, the solution to the equation $-y - 8\frac{2}{7} = 0$ is $y = -8\frac{2}{7}$ .

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Solve the linear equation −y−827=0-y-8 \frac{2}{7}=0−y−872​=0 for the unknown variable yyy.

STEP 1

Assumptions1. The equation to solve is −y−827=0-y - 8\frac{2}{7} = 0−y−872​=0.2. We need to isolate yyy to find its value.

STEP 2

First, we need to convert the mixed number 8278\frac{2}{7}872​ to an improper fraction to make the calculation easier.827=8+278\frac{2}{7} = 8 + \frac{2}{7}872​=8+72​

STEP 3

To convert the mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.827=8×77+278\frac{2}{7} = \frac{8 \times 7}{7} + \frac{2}{7}872​=78×7​+72​

STEP 4

Complete the multiplication and addition to find the improper fraction.827=567+27=5878\frac{2}{7} = \frac{56}{7} + \frac{2}{7} = \frac{58}{7}872​=756​+72​=758​

STEP 5

Now that we have the mixed number as an improper fraction, we can rewrite the equation.−y−587=0-y - \frac{58}{7} = 0−y−758​=0

STEP 6

To isolate yyy, we need to add 587\frac{58}{7}758​ to both sides of the equation.−y−587+587=0+587-y - \frac{58}{7} + \frac{58}{7} = 0 + \frac{58}{7}−y−758​+758​=0+758​

STEP 7

Simplify both sides of the equation.−y=587-y = \frac{58}{7}−y=758​

STEP 8

To find the value of yyy, we need to multiply both sides of the equation by −1-1−1 to get a positive yyy.−1×(−y)=−1×587-1 \times (-y) = -1 \times \frac{58}{7}−1×(−y)=−1×758​

STEP 9

Simplify both sides of the equation to find the value of yyy.y=−587y = -\frac{58}{7}y=−758​

STEP 10

The value of yyy is −587-\frac{58}{7}−758​, which can also be written as a mixed number.y=−827y = -8\frac{2}{7}y=−872​Therefore, the solution to the equation −y−827=0-y - 8\frac{2}{7} = 0−y−872​=0 is y=−827y = -8\frac{2}{7}y=−872​.

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Solve the linear equation $-y-8 \frac{2}{7}=0$ for the unknown variable $y$ .

Assumptions
1. The equation to solve is $-y - 8\frac{2}{7} = 0$ .
2. We need to isolate $y$ to find its value.

First, we need to convert the mixed number $8\frac{2}{7}$ to an improper fraction to make the calculation easier.
$8\frac{2}{7} = 8 + \frac{2}{7}$

To convert the mixed number to an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.
$8\frac{2}{7} = \frac{8 \times 7}{7} + \frac{2}{7}$

Complete the multiplication and addition to find the improper fraction.
$8\frac{2}{7} = \frac{56}{7} + \frac{2}{7} = \frac{58}{7}$

Now that we have the mixed number as an improper fraction, we can rewrite the equation.
$-y - \frac{58}{7} = 0$

To isolate $y$ , we need to add $\frac{58}{7}$ to both sides of the equation.
$-y - \frac{58}{7} + \frac{58}{7} = 0 + \frac{58}{7}$

Simplify both sides of the equation.
$-y = \frac{58}{7}$

To find the value of $y$ , we need to multiply both sides of the equation by $-1$ to get a positive $y$ .
$-1 \times (-y) = -1 \times \frac{58}{7}$

Simplify both sides of the equation to find the value of $y$ .
$y = -\frac{58}{7}$

The value of $y$ is $-\frac{58}{7}$ , which can also be written as a mixed number.
$y = -8\frac{2}{7}$
Therefore, the solution to the equation $-y - 8\frac{2}{7} = 0$ is $y = -8\frac{2}{7}$ .