Solve B={(-1/3)-[(1/5)+(11/3)]-2/5}e

$$B = \{ ( - \frac { 1 } { 3 } ) - [ ( \frac { 1 } { 5 } ) + ( 1 \frac { 1 } { 3 } ) ] - \frac { 2 } { 5 } \} e$$

Solve for B

$$B=-\frac{34e}{15}\approx -6.161438811$$

Steps for Solving Linear Equation

Multiply 1 and 3 to get 3.

$$B=\left(-\frac{1}{3}-\left(\frac{1}{5}+\frac{3+1}{3}\right)-\frac{2}{5}\right)e$$

Add 3 and 1 to get 4.

$$B=\left(-\frac{1}{3}-\left(\frac{1}{5}+\frac{4}{3}\right)-\frac{2}{5}\right)e$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{4}{3} to fractions with denominator 15.

$$B=\left(-\frac{1}{3}-\left(\frac{3}{15}+\frac{20}{15}\right)-\frac{2}{5}\right)e$$

Since \frac{3}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$B=\left(-\frac{1}{3}-\frac{3+20}{15}-\frac{2}{5}\right)e$$

Add 3 and 20 to get 23.

$$B=\left(-\frac{1}{3}-\frac{23}{15}-\frac{2}{5}\right)e$$

Least common multiple of 3 and 15 is 15. Convert -\frac{1}{3} and \frac{23}{15} to fractions with denominator 15.

$$B=\left(-\frac{5}{15}-\frac{23}{15}-\frac{2}{5}\right)e$$

Since -\frac{5}{15} and \frac{23}{15} have the same denominator, subtract them by subtracting their numerators.

$$B=\left(\frac{-5-23}{15}-\frac{2}{5}\right)e$$

Subtract 23 from -5 to get -28.

$$B=\left(-\frac{28}{15}-\frac{2}{5}\right)e$$

Least common multiple of 15 and 5 is 15. Convert -\frac{28}{15} and \frac{2}{5} to fractions with denominator 15.

$$B=\left(-\frac{28}{15}-\frac{6}{15}\right)e$$

Since -\frac{28}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$B=\frac{-28-6}{15}e$$

Subtract 6 from -28 to get -34.

$$B=-\frac{34}{15}e$$

Assign B

$$B≔-\frac{34e}{15}$$