Solve for x x-5/6=7/8

$x - \frac{5}{6} = \frac{7}{8}$

Step 1

Add $\frac{5}{6}$ to both sides of the equation.

$x = \frac{7}{8} + \frac{5}{6}$

Step 2

To write $\frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{7}{8} \cdot \frac{3}{3} + \frac{5}{6}$

Step 3

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x = \frac{7}{8} \cdot \frac{3}{3} + \frac{5}{6} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{8}$ by $\frac{3}{3}$ .

$x = \frac{7 \cdot 3}{8 \cdot 3} + \frac{5}{6} \cdot \frac{4}{4}$

Multiply $8$ by $3$ .

$x = \frac{7 \cdot 3}{24} + \frac{5}{6} \cdot \frac{4}{4}$

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$x = \frac{7 \cdot 3}{24} + \frac{5 \cdot 4}{6 \cdot 4}$

Multiply $6$ by $4$ .

$x = \frac{7 \cdot 3}{24} + \frac{5 \cdot 4}{24}$

Step 5

Combine the numerators over the common denominator.

$x = \frac{7 \cdot 3 + 5 \cdot 4}{24}$

Step 6

Simplify the numerator.

Multiply $7$ by $3$ .

$x = \frac{21 + 5 \cdot 4}{24}$

Multiply $5$ by $4$ .

$x = \frac{21 + 20}{24}$

Add $21$ and $20$ .

$x = \frac{41}{24}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{41}{24}$

Decimal Form:

$x = 1.708\overline{3}$

Mixed Number Form:

$x = 1 \frac{17}{24}$