Algebra Examples

$- \frac{9}{5} x + \frac{3}{5} y = 2$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{9}{5}$ .

$- \frac{x \cdot 9}{5} + \frac{3}{5} y = 2$

Step 1.2

Move $9$ to the left of $x$ .

$- \frac{9 \cdot x}{5} + \frac{3}{5} y = 2$

Step 1.3

Combine $\frac{3}{5}$ and $y$ .

$- \frac{9 x}{5} + \frac{3 y}{5} = 2$

Step 2

Subtract $\frac{3 y}{5}$ from both sides of the equation.

$- \frac{9 x}{5} = 2 - \frac{3 y}{5}$

Step 3

Multiply both sides of the equation by $- \frac{5}{9}$ .

$- \frac{5}{9} (- \frac{9 x}{5}) = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{5}{9} (- \frac{9 x}{5})$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{5}{9}$ into the numerator.

$\frac{- 5}{9} (- \frac{9 x}{5}) = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.1.2

Move the leading negative in $- \frac{9 x}{5}$ into the numerator.

$\frac{- 5}{9} \cdot \frac{- 9 x}{5} = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{9} \cdot \frac{- 9 x}{5} = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{9} \cdot \frac{- 9 x}{5} = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{9} (- 9 x) = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.2

Cancel the common factor of $9$ .

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Step 4.1.1.2.1

Factor $9$ out of $- 9 x$ .

$\frac{- 1}{9} (9 (- x)) = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{9} (9 (- x)) = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{5}{9} (2 - \frac{3 y}{5})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{5}{9} (2 - \frac{3 y}{5})$ .

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Step 4.2.1.1

Apply the distributive property.

$x = - \frac{5}{9} \cdot 2 - \frac{5}{9} (- \frac{3 y}{5})$

Step 4.2.1.2

Multiply $- \frac{5}{9} \cdot 2$ .

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Step 4.2.1.2.1

Multiply $2$ by $- 1$ .

$x = - 2 (\frac{5}{9}) - \frac{5}{9} (- \frac{3 y}{5})$

Step 4.2.1.2.2

Combine $- 2$ and $\frac{5}{9}$ .

$x = \frac{- 2 \cdot 5}{9} - \frac{5}{9} (- \frac{3 y}{5})$

Step 4.2.1.2.3

Multiply $- 2$ by $5$ .

$x = \frac{- 10}{9} - \frac{5}{9} (- \frac{3 y}{5})$

Step 4.2.1.3

Simplify terms.

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Step 4.2.1.3.1

Cancel the common factor of $5$ .

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Step 4.2.1.3.1.1

Move the leading negative in $- \frac{5}{9}$ into the numerator.

$x = \frac{- 10}{9} + \frac{- 5}{9} (- \frac{3 y}{5})$

Step 4.2.1.3.1.2

Move the leading negative in $- \frac{3 y}{5}$ into the numerator.

$x = \frac{- 10}{9} + \frac{- 5}{9} \cdot \frac{- 3 y}{5}$

Step 4.2.1.3.1.3

Factor $5$ out of $- 5$ .

$x = \frac{- 10}{9} + \frac{5 (- 1)}{9} \cdot \frac{- 3 y}{5}$

Step 4.2.1.3.1.4

Cancel the common factor.

$x = \frac{- 10}{9} + \frac{5 \cdot - 1}{9} \cdot \frac{- 3 y}{5}$

Step 4.2.1.3.1.5

Rewrite the expression.

$x = \frac{- 10}{9} + \frac{- 1}{9} (- 3 y)$

Step 4.2.1.3.2

Cancel the common factor of $3$ .

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Step 4.2.1.3.2.1

Factor $3$ out of $9$ .

$x = \frac{- 10}{9} + \frac{- 1}{3 (3)} (- 3 y)$

Step 4.2.1.3.2.2

Factor $3$ out of $- 3 y$ .

$x = \frac{- 10}{9} + \frac{- 1}{3 (3)} (3 (- y))$

Step 4.2.1.3.2.3

Cancel the common factor.

$x = \frac{- 10}{9} + \frac{- 1}{3 \cdot 3} (3 (- y))$

Step 4.2.1.3.2.4

Rewrite the expression.

$x = \frac{- 10}{9} + \frac{- 1}{3} (- y)$

Step 4.2.1.3.3

Combine $\frac{- 1}{3}$ and $y$ .

$x = \frac{- 10}{9} - \frac{- y}{3}$

Step 4.2.1.4

Simplify each term.

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Step 4.2.1.4.1

Move the negative in front of the fraction.

$x = - \frac{10}{9} - \frac{- y}{3}$

Step 4.2.1.4.2

Move the negative in front of the fraction.

$x = - \frac{10}{9} - - \frac{y}{3}$

Step 4.2.1.4.3

Multiply $- - \frac{y}{3}$ .

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Step 4.2.1.4.3.1

Multiply $- 1$ by $- 1$ .

$x = - \frac{10}{9} + 1 \frac{y}{3}$

Step 4.2.1.4.3.2

Multiply $\frac{y}{3}$ by $1$ .

$x = - \frac{10}{9} + \frac{y}{3}$

Step 5

Reorder $- \frac{10}{9}$ and $\frac{y}{3}$ .

$x = \frac{y}{3} - \frac{10}{9}$