Solve for x 1 1/3+x=3 2/3

$1 \frac{1}{3} + x = 3 \frac{2}{3}$

Step 1

Simplify the left side.

Convert $1 \frac{1}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$1 + \frac{1}{3} + x = 3 \frac{2}{3}$

Add $1$ and $\frac{1}{3}$ .

Write $1$ as a fraction with a common denominator.

$\frac{3}{3} + \frac{1}{3} + x = 3 \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{3 + 1}{3} + x = 3 \frac{2}{3}$

Add $3$ and $1$ .

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

Step 2

Simplify the right side.

Convert $3 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $3$ and $\frac{2}{3}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{4}{3} + x = \frac{9 + 2}{3}$

Add $9$ and $2$ .

$\frac{4}{3} + x = \frac{11}{3}$

Step 3

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

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

$x = \frac{11}{3} - \frac{4}{3}$

Combine the numerators over the common denominator.

$x = \frac{11 - 4}{3}$

Subtract $4$ from $11$ .

$x = \frac{7}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{3}$

Decimal Form:

$x = 2.\overline{3}$

Mixed Number Form:

$x = 2 \frac{1}{3}$

Solve for x 1 1/3+x=3 2/3

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