Solve 2-[11/3-2-(13-5*1/3)]=3*(7-31/3)-3

$$2 - [ \frac { 11 } { 3 } - 2 - ( 13 - 5 \cdot \frac { 1 } { 3 } ) ] = 3 \cdot ( 7 - 3 \frac { 1 } { 3 } ) - 3$$

Verify

Solution Steps

Multiply both sides of the equation by 3.

$$6-3\left(\frac{11}{3}-2-\left(13-5\times \frac{1}{3}\right)\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Convert 2 to fraction \frac{6}{3}.

$$6-3\left(\frac{11}{3}-\frac{6}{3}-\left(13-5\times \frac{1}{3}\right)\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Since \frac{11}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$6-3\left(\frac{11-6}{3}-\left(13-5\times \frac{1}{3}\right)\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Subtract 6 from 11 to get 5.

$$6-3\left(\frac{5}{3}-\left(13-5\times \frac{1}{3}\right)\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Multiply 5 and \frac{1}{3} to get \frac{5}{3}.

$$6-3\left(\frac{5}{3}-\left(13-\frac{5}{3}\right)\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Convert 13 to fraction \frac{39}{3}.

$$6-3\left(\frac{5}{3}-\left(\frac{39}{3}-\frac{5}{3}\right)\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Since \frac{39}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$6-3\left(\frac{5}{3}-\frac{39-5}{3}\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Subtract 5 from 39 to get 34.

$$6-3\left(\frac{5}{3}-\frac{34}{3}\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Since \frac{5}{3} and \frac{34}{3} have the same denominator, subtract them by subtracting their numerators.

$$6-3\times \frac{5-34}{3}=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Subtract 34 from 5 to get -29.

$$6-3\left(-\frac{29}{3}\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Cancel out 3 and 3.

$$6-\left(-29\right)=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

The opposite of -29 is 29.

$$6+29=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Add 6 and 29 to get 35.

$$35=9\left(7-\frac{3\times 3+1}{3}\right)-9$$

Multiply 3 and 3 to get 9.

$$35=9\left(7-\frac{9+1}{3}\right)-9$$

Add 9 and 1 to get 10.

$$35=9\left(7-\frac{10}{3}\right)-9$$

Convert 7 to fraction \frac{21}{3}.

$$35=9\left(\frac{21}{3}-\frac{10}{3}\right)-9$$

Since \frac{21}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$35=9\times \frac{21-10}{3}-9$$

Subtract 10 from 21 to get 11.

$$35=9\times \frac{11}{3}-9$$

Express 9\times \frac{11}{3} as a single fraction.

$$35=\frac{9\times 11}{3}-9$$

Multiply 9 and 11 to get 99.

$$35=\frac{99}{3}-9$$

Divide 99 by 3 to get 33.

$$35=33-9$$

Subtract 9 from 33 to get 24.

$$35=24$$

Compare 35 and 24.

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