Solve 2/3+1/2frac{2{5}}-1/x=1/3-frac{1}{2frac{2}{3}}

$$\frac { 2 } { 3 } + \frac { 1 } { 2 \frac { 2 } { 5 } } - \frac { 1 } { x } = \frac { 1 } { 3 } - \frac { 1 } { 2 \frac { 2 } { 3 } }$$

Solve for x

$$x=\frac{8}{9}\approx 0.888888889$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x, the least common multiple of 3,x.

$$3x\times \frac{2}{3}+\frac{5}{4}x-3=3x\times \frac{1}{3}-\frac{9}{8}x$$

Cancel out 3 and 3.

$$2x+\frac{5}{4}x-3=3x\times \frac{1}{3}-\frac{9}{8}x$$

Combine 2x and \frac{5}{4}x to get \frac{13}{4}x.

$$\frac{13}{4}x-3=3x\times \frac{1}{3}-\frac{9}{8}x$$

Cancel out 3 and 3.

$$\frac{13}{4}x-3=x-\frac{9}{8}x$$

Combine x and -\frac{9}{8}x to get -\frac{1}{8}x.

$$\frac{13}{4}x-3=-\frac{1}{8}x$$

Add \frac{1}{8}x to both sides.

$$\frac{13}{4}x-3+\frac{1}{8}x=0$$

Combine \frac{13}{4}x and \frac{1}{8}x to get \frac{27}{8}x.

$$\frac{27}{8}x-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$\frac{27}{8}x=3$$

Multiply both sides by \frac{8}{27}, the reciprocal of \frac{27}{8}.

$$x=3\times \frac{8}{27}$$

Express 3\times \frac{8}{27} as a single fraction.

$$x=\frac{3\times 8}{27}$$

Multiply 3 and 8 to get 24.

$$x=\frac{24}{27}$$

Reduce the fraction \frac{24}{27} to lowest terms by extracting and canceling out 3.

$$x=\frac{8}{9}$$