Basic Math Examples

$\frac{5 (2 - y)}{2} = y$

Step 1

Multiply both sides by $2$ .

$\frac{5 (2 - y)}{2} \cdot 2 = y \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5 (2 - y)}{2} \cdot 2$ .

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Step 2.1.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{5 (2 - y)}{2} \cdot 2 = y \cdot 2$

Step 2.1.1.1.2

Rewrite the expression.

$5 (2 - y) = y \cdot 2$

$5 (2 - y) = y \cdot 2$

Step 2.1.1.2

Apply the distributive property.

$5 \cdot 2 + 5 (- y) = y \cdot 2$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Multiply $5$ by $2$ .

$10 + 5 (- y) = y \cdot 2$

Step 2.1.1.3.2

Multiply $- 1$ by $5$ .

$10 - 5 y = y \cdot 2$

Step 2.1.1.3.3

Reorder $10$ and $- 5 y$ .

$- 5 y + 10 = y \cdot 2$

$- 5 y + 10 = y \cdot 2$

$- 5 y + 10 = y \cdot 2$

$- 5 y + 10 = y \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Move $2$ to the left of $y$ .

$- 5 y + 10 = 2 y$

$- 5 y + 10 = 2 y$

$- 5 y + 10 = 2 y$

Step 3

Solve for $y$ .

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Step 3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.1.1

Subtract $2 y$ from both sides of the equation.

$- 5 y + 10 - 2 y = 0$

Step 3.1.2

Subtract $2 y$ from $- 5 y$ .

$- 7 y + 10 = 0$

$- 7 y + 10 = 0$

Step 3.2

Subtract $10$ from both sides of the equation.

$- 7 y = - 10$

Step 3.3

Divide each term in $- 7 y = - 10$ by $- 7$ and simplify.

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Step 3.3.1

Divide each term in $- 7 y = - 10$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 10}{- 7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 10}{- 7}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 10}{- 7}$

$y = \frac{- 10}{- 7}$

$y = \frac{- 10}{- 7}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$y = \frac{10}{7}$

$y = \frac{10}{7}$

$y = \frac{10}{7}$

$y = \frac{10}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{10}{7}$

Decimal Form:

$y = 1.\overline{428571}$

Mixed Number Form:

$y = 1 \frac{3}{7}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$