Algebra Examples

2 w - y = 7 w - 2

$2 w - y = 7 w - 2$

Step 1

Move all terms containing

w

$w$ to the left side of the equation.

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Step 1.1

Subtract

7 w

$7 w$ from both sides of the equation.

2 w - y - 7 w = - 2

$2 w - y - 7 w = - 2$

Step 1.2

Subtract

7 w

$7 w$ from

2 w

$2 w$ .

- 5 w - y = - 2

$- 5 w - y = - 2$

- 5 w - y = - 2

$- 5 w - y = - 2$

Step 2

Add

y

$y$ to both sides of the equation.

- 5 w = - 2 + y

$- 5 w = - 2 + y$

Step 3

Divide each term in

- 5 w = - 2 + y

$- 5 w = - 2 + y$ by

- 5

$- 5$ and simplify.

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Step 3.1

Divide each term in

- 5 w = - 2 + y

$- 5 w = - 2 + y$ by

- 5

$- 5$ .

\frac{- 5 w}{- 5} = \frac{- 2}{- 5} + \frac{y}{- 5}

$\frac{- 5 w}{- 5} = \frac{- 2}{- 5} + \frac{y}{- 5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

- 5

$- 5$ .

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Step 3.2.1.1

Cancel the common factor.

\frac{- 5 w}{- 5} = \frac{- 2}{- 5} + \frac{y}{- 5}

$\frac{- 5 w}{- 5} = \frac{- 2}{- 5} + \frac{y}{- 5}$

Step 3.2.1.2

Divide

w

$w$ by

1

$1$ .

w = \frac{- 2}{- 5} + \frac{y}{- 5}

$w = \frac{- 2}{- 5} + \frac{y}{- 5}$

w = \frac{- 2}{- 5} + \frac{y}{- 5}

$w = \frac{- 2}{- 5} + \frac{y}{- 5}$

w = \frac{- 2}{- 5} + \frac{y}{- 5}

$w = \frac{- 2}{- 5} + \frac{y}{- 5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Dividing two negative values results in a positive value.

w = \frac{2}{5} + \frac{y}{- 5}

$w = \frac{2}{5} + \frac{y}{- 5}$

Step 3.3.1.2

Move the negative in front of the fraction.

w = \frac{2}{5} - \frac{y}{5}

$w = \frac{2}{5} - \frac{y}{5}$

w = \frac{2}{5} - \frac{y}{5}

$w = \frac{2}{5} - \frac{y}{5}$

w = \frac{2}{5} - \frac{y}{5}

$w = \frac{2}{5} - \frac{y}{5}$

w = \frac{2}{5} - \frac{y}{5}

$w = \frac{2}{5} - \frac{y}{5}$