Solve for t (t-2)/12=7/8

$\frac{t - 2}{12} = \frac{7}{8}$

Step 1

Multiply both sides of the equation by $12$ .

$12 \frac{t - 2}{12} = 12 (\frac{7}{8})$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$12 \frac{t - 2}{12} = 12 (\frac{7}{8})$

Rewrite the expression.

$t - 2 = 12 (\frac{7}{8})$

Simplify the right side.

Simplify $12 (\frac{7}{8})$ .

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$t - 2 = 4 (3) \frac{7}{8}$

Factor $4$ out of $8$ .

$t - 2 = 4 \cdot 3 \frac{7}{4 \cdot 2}$

Cancel the common factor.

$t - 2 = 4 \cdot 3 \frac{7}{4 \cdot 2}$

Rewrite the expression.

$t - 2 = 3 (\frac{7}{2})$

Combine $3$ and $\frac{7}{2}$ .

$t - 2 = \frac{3 \cdot 7}{2}$

Multiply $3$ by $7$ .

$t - 2 = \frac{21}{2}$

Step 3

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

Add $2$ to both sides of the equation.

$t = \frac{21}{2} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$t = \frac{21}{2} + 2 \cdot \frac{2}{2}$

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

$t = \frac{21}{2} + \frac{2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$t = \frac{21 + 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$t = \frac{21 + 4}{2}$

Add $21$ and $4$ .

$t = \frac{25}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{25}{2}$

Decimal Form:

$t = 12.5$

Mixed Number Form:

$t = 12 \frac{1}{2}$

Solve for t (t-2)/12=7/8

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