Finite Math Examples

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

Step 1

Multiply both sides of the equation by $- \frac{3}{7}$ .

$- \frac{3}{7} (- \frac{7}{3} x) = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $- \frac{3}{7} (- \frac{7}{3} x)$ .

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Step 2.1.1.1

Combine $x$ and $\frac{7}{3}$ .

$- \frac{3}{7} (- \frac{x \cdot 7}{3}) = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Move the leading negative in $- \frac{3}{7}$ into the numerator.

$\frac{- 3}{7} (- \frac{x \cdot 7}{3}) = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.2.2

Move the leading negative in $- \frac{x \cdot 7}{3}$ into the numerator.

$\frac{- 3}{7} \cdot \frac{- x \cdot 7}{3} = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.2.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{7} \cdot \frac{- x \cdot 7}{3} = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{3 \cdot - 1}{7} \cdot \frac{- x \cdot 7}{3} = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{7} (- x \cdot 7) = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.3

Cancel the common factor of $7$ .

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Step 2.1.1.3.1

Factor $7$ out of $- x \cdot 7$ .

$\frac{- 1}{7} (7 \cdot (- x)) = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{7} (7 \cdot (- x)) = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.3.3

Rewrite the expression.

$- - x = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.1.1.4.2

Multiply $x$ by $1$ .

$x = - \frac{3}{7} (1 - \frac{1}{3} y)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{3}{7} (1 - \frac{1}{3} y)$ .

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Step 2.2.1.1

Simplify terms.

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Step 2.2.1.1.1

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

$x = - \frac{3}{7} (1 - \frac{y}{3})$

Step 2.2.1.1.2

Apply the distributive property.

$x = - \frac{3}{7} \cdot 1 - \frac{3}{7} (- \frac{y}{3})$

Step 2.2.1.1.3

Multiply $- 1$ by $1$ .

$x = - \frac{3}{7} - \frac{3}{7} (- \frac{y}{3})$

Step 2.2.1.1.4

Cancel the common factor of $3$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{3}{7}$ into the numerator.

$x = - \frac{3}{7} + \frac{- 3}{7} (- \frac{y}{3})$

Step 2.2.1.1.4.2

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

$x = - \frac{3}{7} + \frac{- 3}{7} \cdot \frac{- y}{3}$

Step 2.2.1.1.4.3

Factor $3$ out of $- 3$ .

$x = - \frac{3}{7} + \frac{3 (- 1)}{7} \cdot \frac{- y}{3}$

Step 2.2.1.1.4.4

Cancel the common factor.

$x = - \frac{3}{7} + \frac{3 \cdot - 1}{7} \cdot \frac{- y}{3}$

Step 2.2.1.1.4.5

Rewrite the expression.

$x = - \frac{3}{7} + \frac{- 1}{7} (- y)$

Step 2.2.1.1.5

Combine $\frac{- 1}{7}$ and $y$ .

$x = - \frac{3}{7} - \frac{- y}{7}$

Step 2.2.1.2

Simplify each term.

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Step 2.2.1.2.1

Move the negative in front of the fraction.

$x = - \frac{3}{7} - - \frac{y}{7}$

Step 2.2.1.2.2

Multiply $- - \frac{y}{7}$ .

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Step 2.2.1.2.2.1

Multiply $- 1$ by $- 1$ .

$x = - \frac{3}{7} + 1 \frac{y}{7}$

Step 2.2.1.2.2.2

Multiply $\frac{y}{7}$ by $1$ .

$x = - \frac{3}{7} + \frac{y}{7}$

Step 3

Reorder $- \frac{3}{7}$ and $\frac{y}{7}$ .

$x = \frac{y}{7} - \frac{3}{7}$