Solve x-(2/3x-5/11)=8/3

$$x - ( \frac { 2 } { 3 } x - \frac { 5 } { 11 } ) = \frac { 8 } { 3 }$$

Solve for x

$$x = \frac{73}{11} = 6\frac{7}{11} \approx 6.636363636$$

Steps for Solving Linear Equation

To find the opposite of \frac{2}{3}x-\frac{5}{11}, find the opposite of each term.

$$x-\frac{2}{3}x-\left(-\frac{5}{11}\right)=\frac{8}{3}$$

The opposite of -\frac{5}{11} is \frac{5}{11}.

$$x-\frac{2}{3}x+\frac{5}{11}=\frac{8}{3}$$

Combine x and -\frac{2}{3}x to get \frac{1}{3}x.

$$\frac{1}{3}x+\frac{5}{11}=\frac{8}{3}$$

Subtract \frac{5}{11} from both sides.

$$\frac{1}{3}x=\frac{8}{3}-\frac{5}{11}$$

Least common multiple of 3 and 11 is 33. Convert \frac{8}{3} and \frac{5}{11} to fractions with denominator 33.

$$\frac{1}{3}x=\frac{88}{33}-\frac{15}{33}$$

Since \frac{88}{33} and \frac{15}{33} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}x=\frac{88-15}{33}$$

Subtract 15 from 88 to get 73.

$$\frac{1}{3}x=\frac{73}{33}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$x=\frac{73}{33}\times 3$$

Express \frac{73}{33}\times 3 as a single fraction.

$$x=\frac{73\times 3}{33}$$

Multiply 73 and 3 to get 219.

$$x=\frac{219}{33}$$

Reduce the fraction \frac{219}{33} to lowest terms by extracting and canceling out 3.

$$x=\frac{73}{11}$$