Solve for a (a-6)/5=7/12

$\frac{a - 6}{5} = \frac{7}{12}$

Step 1

Multiply both sides of the equation by $5$ .

$5 \frac{a - 6}{5} = 5 (\frac{7}{12})$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{a - 6}{5} = 5 (\frac{7}{12})$

Rewrite the expression.

$a - 6 = 5 (\frac{7}{12})$

Simplify the right side.

Multiply $5 (\frac{7}{12})$ .

Combine $5$ and $\frac{7}{12}$ .

$a - 6 = \frac{5 \cdot 7}{12}$

Multiply $5$ by $7$ .

$a - 6 = \frac{35}{12}$

Step 3

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

Add $6$ to both sides of the equation.

$a = \frac{35}{12} + 6$

To write $6$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$a = \frac{35}{12} + 6 \cdot \frac{12}{12}$

Combine $6$ and $\frac{12}{12}$ .

$a = \frac{35}{12} + \frac{6 \cdot 12}{12}$

Combine the numerators over the common denominator.

$a = \frac{35 + 6 \cdot 12}{12}$

Simplify the numerator.

Multiply $6$ by $12$ .

$a = \frac{35 + 72}{12}$

Add $35$ and $72$ .

$a = \frac{107}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{107}{12}$

Decimal Form:

$a = 8.91\overline{6}$

Mixed Number Form:

$a = 8 \frac{11}{12}$