Finite Math Examples

$2 x - 3 y = 8$

Step 1

Solve for $y$ .

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Step 1.1

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

$- 3 y = 8 - 2 x$

Step 1.2

Divide each term in $- 3 y = 8 - 2 x$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 y = 8 - 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{8}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{8}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{- 3} + \frac{- 2 x}{- 3}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{8}{3} + \frac{- 2 x}{- 3}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{8}{3} + \frac{2 x}{3}$

Step 2

Set $8$ equal to $0$ .

$- \frac{8}{3} + \frac{2 x}{3} = 0$

Step 3

Solve for $x$ .

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Step 3.1

Add $\frac{8}{3}$ to both sides of the equation.

$\frac{2 x}{3} = \frac{8}{3}$

Step 3.2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$2 x = 8$

Step 3.3

Divide each term in $2 x = 8$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $8$ by $2$ .

$x = 4$

Step 4