Solve A=(1/2+T/B)*B/11

$$A = ( \frac { 1 } { 2 } + \frac { T } { B } ) \times \frac { B } { 11 }$$

Solve for A

$$A=\frac{B+2T}{22}$$

$$B\neq 0$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and B is 2B. Multiply \frac{1}{2} times \frac{B}{B}. Multiply \frac{T}{B} times \frac{2}{2}.

$$A=\left(\frac{B}{2B}+\frac{2T}{2B}\right)\times \frac{B}{11}$$

Since \frac{B}{2B} and \frac{2T}{2B} have the same denominator, add them by adding their numerators.

$$A=\frac{B+2T}{2B}\times \frac{B}{11}$$

Multiply \frac{B+2T}{2B} times \frac{B}{11} by multiplying numerator times numerator and denominator times denominator.

$$A=\frac{\left(B+2T\right)B}{2B\times 11}$$

Cancel out B in both numerator and denominator.

$$A=\frac{B+2T}{2\times 11}$$

Multiply 2 and 11 to get 22.

$$A=\frac{B+2T}{22}$$

Divide each term of B+2T by 22 to get \frac{1}{22}B+\frac{1}{11}T.

$$A=\frac{1}{22}B+\frac{1}{11}T$$

Solve for B

$$B=22A-2T$$

$$A\neq \frac{T}{11}$$