Finite Math Examples

$\frac{2}{3} + \frac{1}{2} t = \frac{1}{3}$

Step 1

Combine $\frac{1}{2}$ and $t$ .

$\frac{2}{3} + \frac{t}{2} = \frac{1}{3}$

Step 2

Move all terms not containing $t$ to the right side of the equation.

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Step 2.1

Subtract $\frac{2}{3}$ from both sides of the equation.

$\frac{t}{2} = \frac{1}{3} - \frac{2}{3}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{t}{2} = \frac{1 - 2}{3}$

Step 2.3

Subtract $2$ from $1$ .

$\frac{t}{2} = \frac{- 1}{3}$

Step 2.4

Move the negative in front of the fraction.

$\frac{t}{2} = - \frac{1}{3}$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{t}{2} = 2 (- \frac{1}{3})$

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

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

$2 \frac{t}{2} = 2 (- \frac{1}{3})$

Step 4.1.1.2

Rewrite the expression.

$t = 2 (- \frac{1}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $2 (- \frac{1}{3})$ .

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Step 4.2.1.1

Multiply $2 (- \frac{1}{3})$ .

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Step 4.2.1.1.1

Multiply $- 1$ by $2$ .

$t = - 2 (\frac{1}{3})$

Step 4.2.1.1.2

Combine $- 2$ and $\frac{1}{3}$ .

$t = \frac{- 2}{3}$

Step 4.2.1.2

Move the negative in front of the fraction.

$t = - \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{2}{3}$

Decimal Form:

$t = - 0.\overline{6}$