Solve for x x+4/3=31/2

$x + \frac{4}{3} = \frac{31}{2}$

Step 1

Subtract $\frac{4}{3}$ from both sides of the equation.

$x = \frac{31}{2} - \frac{4}{3}$

Step 2

To write $\frac{31}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{31}{2} \cdot \frac{3}{3} - \frac{4}{3}$

Step 3

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{31}{2} \cdot \frac{3}{3} - \frac{4}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{31}{2}$ by $\frac{3}{3}$ .

$x = \frac{31 \cdot 3}{2 \cdot 3} - \frac{4}{3} \cdot \frac{2}{2}$

Multiply $2$ by $3$ .

$x = \frac{31 \cdot 3}{6} - \frac{4}{3} \cdot \frac{2}{2}$

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$x = \frac{31 \cdot 3}{6} - \frac{4 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$x = \frac{31 \cdot 3}{6} - \frac{4 \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$x = \frac{31 \cdot 3 - 4 \cdot 2}{6}$

Step 6

Simplify the numerator.

Multiply $31$ by $3$ .

$x = \frac{93 - 4 \cdot 2}{6}$

Multiply $- 4$ by $2$ .

$x = \frac{93 - 8}{6}$

Subtract $8$ from $93$ .

$x = \frac{85}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{85}{6}$

Decimal Form:

$x = 14.1\overline{6}$

Mixed Number Form:

$x = 14 \frac{1}{6}$