QuestionIsolate $y$ in the equation $-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}$ . Express your answer as an integer.

Studdy Solution

STEP 1

Assumptions1. The equation is $-\frac{5}{6} y-\frac{1}{5} y=\frac{4}{3}-\frac{1}{5}$ . We need to isolate the variable $y$ .

STEP 2

First, we need to combine like terms on both sides of the equation. On the left side, we have $-\frac{5}{6} y$ and $-\frac{1}{5} y$ . On the right side, we have $\frac{4}{}$ and $-\frac{1}{5}$ .

STEP 3

To combine $-\frac{5}{6} y$ and $-\frac{1}{5} y$ , we need to find a common denominator. The least common multiple of6 and5 is30.
$-\frac{5}{6} y-\frac{1}{5} y = -\frac{25}{30} y - \frac{6}{30} y$

STEP 4

Now, combine the terms on the left side of the equation.
$-\frac{25}{30} y - \frac{6}{30} y = -\frac{31}{30} y$

STEP 5

Similarly, combine the terms on the right side of the equation.
$\frac{4}{3} - \frac{1}{5} = \frac{20}{15} - \frac{3}{15} = \frac{17}{15}$

STEP 6

So, the equation becomes $-\frac{31}{30} y = \frac{17}{15}$

STEP 7

To isolate $y$ , divide both sides of the equation by $-\frac{31}{30}$ .
$y = \frac{\frac{17}{15}}{-\frac{31}{30}}$

STEP 8

This simplifies to $y = \frac{17}{15} \times \frac{-30}{31}$

STEP 9

implify the expression to get the final answer.
$y = \frac{-17}{31}$ So, $y = -\frac{17}{31}$ is the solution to the equation.

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QuestionIsolate $y$ in the equation $-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}$ . Express your answer as an integer.

Studdy Solution

STEP 1

Assumptions1. The equation is $-\frac{5}{6} y-\frac{1}{5} y=\frac{4}{3}-\frac{1}{5}$ . We need to isolate the variable $y$ .

STEP 2

First, we need to combine like terms on both sides of the equation. On the left side, we have $-\frac{5}{6} y$ and $-\frac{1}{5} y$ . On the right side, we have $\frac{4}{}$ and $-\frac{1}{5}$ .

STEP 3

To combine $-\frac{5}{6} y$ and $-\frac{1}{5} y$ , we need to find a common denominator. The least common multiple of6 and5 is30.
$-\frac{5}{6} y-\frac{1}{5} y = -\frac{25}{30} y - \frac{6}{30} y$

STEP 4

Now, combine the terms on the left side of the equation.
$-\frac{25}{30} y - \frac{6}{30} y = -\frac{31}{30} y$

STEP 5

Similarly, combine the terms on the right side of the equation.
$\frac{4}{3} - \frac{1}{5} = \frac{20}{15} - \frac{3}{15} = \frac{17}{15}$

STEP 6

So, the equation becomes $-\frac{31}{30} y = \frac{17}{15}$

STEP 7

To isolate $y$ , divide both sides of the equation by $-\frac{31}{30}$ .
$y = \frac{\frac{17}{15}}{-\frac{31}{30}}$

STEP 8

This simplifies to $y = \frac{17}{15} \times \frac{-30}{31}$

STEP 9

implify the expression to get the final answer.
$y = \frac{-17}{31}$ So, $y = -\frac{17}{31}$ is the solution to the equation.

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QuestionIsolate yyy in the equation −56y−15y=43−15-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}−65​y−51​y=34​−51​. Express your answer as an integer.

Studdy Solution

STEP 1

Assumptions1. The equation is −56y−15y=43−15-\frac{5}{6} y-\frac{1}{5} y=\frac{4}{3}-\frac{1}{5}−65​y−51​y=34​−51​ . We need to isolate the variable yyy.

STEP 2

First, we need to combine like terms on both sides of the equation. On the left side, we have −56y-\frac{5}{6} y−65​y and −15y-\frac{1}{5} y−51​y. On the right side, we have 4\frac{4}{}4​ and −15-\frac{1}{5}−51​.

STEP 3

To combine −56y-\frac{5}{6} y−65​y and −15y-\frac{1}{5} y−51​y, we need to find a common denominator. The least common multiple of6 and5 is30.−56y−15y=−2530y−630y-\frac{5}{6} y-\frac{1}{5} y = -\frac{25}{30} y - \frac{6}{30} y−65​y−51​y=−3025​y−306​y

STEP 4

Now, combine the terms on the left side of the equation.−2530y−630y=−3130y-\frac{25}{30} y - \frac{6}{30} y = -\frac{31}{30} y−3025​y−306​y=−3031​y

STEP 5

Similarly, combine the terms on the right side of the equation.43−15=2015−315=1715\frac{4}{3} - \frac{1}{5} = \frac{20}{15} - \frac{3}{15} = \frac{17}{15}34​−51​=1520​−153​=1517​

STEP 6

So, the equation becomes−3130y=1715-\frac{31}{30} y = \frac{17}{15}−3031​y=1517​

STEP 7

To isolate yyy, divide both sides of the equation by −3130-\frac{31}{30}−3031​.y=1715−3130y = \frac{\frac{17}{15}}{-\frac{31}{30}}y=−3031​1517​​

STEP 8

This simplifies toy=1715×−3031y = \frac{17}{15} \times \frac{-30}{31}y=1517​×31−30​

STEP 9

implify the expression to get the final answer.y=−1731y = \frac{-17}{31}y=31−17​So, y=−1731y = -\frac{17}{31}y=−3117​ is the solution to the equation.

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QuestionIsolate $y$ in the equation $-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}$ . Express your answer as an integer.

Assumptions1. The equation is $-\frac{5}{6} y-\frac{1}{5} y=\frac{4}{3}-\frac{1}{5}$ . We need to isolate the variable $y$ .

First, we need to combine like terms on both sides of the equation. On the left side, we have $-\frac{5}{6} y$ and $-\frac{1}{5} y$ . On the right side, we have $\frac{4}{}$ and $-\frac{1}{5}$ .

To combine $-\frac{5}{6} y$ and $-\frac{1}{5} y$ , we need to find a common denominator. The least common multiple of6 and5 is30.
$-\frac{5}{6} y-\frac{1}{5} y = -\frac{25}{30} y - \frac{6}{30} y$

Now, combine the terms on the left side of the equation.
$-\frac{25}{30} y - \frac{6}{30} y = -\frac{31}{30} y$

Similarly, combine the terms on the right side of the equation.
$\frac{4}{3} - \frac{1}{5} = \frac{20}{15} - \frac{3}{15} = \frac{17}{15}$

So, the equation becomes $-\frac{31}{30} y = \frac{17}{15}$

To isolate $y$ , divide both sides of the equation by $-\frac{31}{30}$ .
$y = \frac{\frac{17}{15}}{-\frac{31}{30}}$

This simplifies to $y = \frac{17}{15} \times \frac{-30}{31}$

implify the expression to get the final answer.
$y = \frac{-17}{31}$ So, $y = -\frac{17}{31}$ is the solution to the equation.