Solve for x x-3/4=5/6

$x - \frac{3}{4} = \frac{5}{6}$

Step 1

Add $\frac{3}{4}$ to both sides of the equation.

$x = \frac{5}{6} + \frac{3}{4}$

Step 2

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{5}{6} \cdot \frac{2}{2} + \frac{3}{4}$

Step 3

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{5}{6} \cdot \frac{2}{2} + \frac{3}{4} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$x = \frac{5 \cdot 2}{6 \cdot 2} + \frac{3}{4} \cdot \frac{3}{3}$

Multiply $6$ by $2$ .

$x = \frac{5 \cdot 2}{12} + \frac{3}{4} \cdot \frac{3}{3}$

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$x = \frac{5 \cdot 2}{12} + \frac{3 \cdot 3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$x = \frac{5 \cdot 2}{12} + \frac{3 \cdot 3}{12}$

Step 5

Combine the numerators over the common denominator.

$x = \frac{5 \cdot 2 + 3 \cdot 3}{12}$

Step 6

Simplify the numerator.

Multiply $5$ by $2$ .

$x = \frac{10 + 3 \cdot 3}{12}$

Multiply $3$ by $3$ .

$x = \frac{10 + 9}{12}$

Add $10$ and $9$ .

$x = \frac{19}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{12}$

Decimal Form:

$x = 1.58\overline{3}$

Mixed Number Form:

$x = 1 \frac{7}{12}$