Solve (b/12+1/2x):21/2=11/12

$$( \frac { b } { 12 } + \frac { 1 } { 2 } x ) : 2 \frac { 1 } { 2 } = \frac { 11 } { 12 }$$

Solve for b

$$b=\frac{55}{2}-6x$$

Steps for Solving Linear Equation

Multiply 2 and 2 to get 4.

$$\frac{\frac{b}{12}+\frac{1}{2}x}{\frac{4+1}{2}}=\frac{11}{12}$$

Add 4 and 1 to get 5.

$$\frac{\frac{b}{12}+\frac{1}{2}x}{\frac{5}{2}}=\frac{11}{12}$$

Divide each term of \frac{b}{12}+\frac{1}{2}x by \frac{5}{2} to get \frac{\frac{b}{12}}{\frac{5}{2}}+\frac{\frac{1}{2}x}{\frac{5}{2}}.

$$\frac{\frac{b}{12}}{\frac{5}{2}}+\frac{\frac{1}{2}x}{\frac{5}{2}}=\frac{11}{12}$$

Divide \frac{1}{2}x by \frac{5}{2} to get \frac{1}{5}x.

$$\frac{\frac{b}{12}}{\frac{5}{2}}+\frac{1}{5}x=\frac{11}{12}$$

Subtract \frac{1}{5}x from both sides.

$$\frac{\frac{b}{12}}{\frac{5}{2}}=\frac{11}{12}-\frac{1}{5}x$$

Reorder the terms.

$$\frac{b}{\frac{5}{2}\times 12}=-\frac{1}{5}x+\frac{11}{12}$$

Multiply \frac{5}{2} and 12 to get 30.

$$\frac{b}{30}=-\frac{1}{5}x+\frac{11}{12}$$

Multiply both sides of the equation by 60, the least common multiple of 30,5,12.

$$2b=-12x+55$$

The equation is in standard form.

$$2b=55-12x$$

Divide both sides by 2.

$$\frac{2b}{2}=\frac{55-12x}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$b=\frac{55-12x}{2}$$

Divide -12x+55 by 2.

$$b=\frac{55}{2}-6x$$

Solve for x

$$x=-\frac{b}{6}+\frac{55}{12}$$

Steps for Solving Linear Equation

Multiply 2 and 2 to get 4.

$$\frac{\frac{b}{12}+\frac{1}{2}x}{\frac{4+1}{2}}=\frac{11}{12}$$

Add 4 and 1 to get 5.

$$\frac{\frac{b}{12}+\frac{1}{2}x}{\frac{5}{2}}=\frac{11}{12}$$

Divide each term of \frac{b}{12}+\frac{1}{2}x by \frac{5}{2} to get \frac{\frac{b}{12}}{\frac{5}{2}}+\frac{\frac{1}{2}x}{\frac{5}{2}}.

$$\frac{\frac{b}{12}}{\frac{5}{2}}+\frac{\frac{1}{2}x}{\frac{5}{2}}=\frac{11}{12}$$

Divide \frac{1}{2}x by \frac{5}{2} to get \frac{1}{5}x.

$$\frac{\frac{b}{12}}{\frac{5}{2}}+\frac{1}{5}x=\frac{11}{12}$$

Subtract \frac{\frac{b}{12}}{\frac{5}{2}} from both sides.

$$\frac{1}{5}x=\frac{11}{12}-\frac{\frac{b}{12}}{\frac{5}{2}}$$

Reorder the terms.

$$\frac{1}{5}x=-\frac{b}{\frac{5}{2}\times 12}+\frac{11}{12}$$

Multiply \frac{5}{2} and 12 to get 30.

$$\frac{1}{5}x=-\frac{b}{30}+\frac{11}{12}$$

Multiply both sides by 5.

$$\frac{\frac{1}{5}x}{\frac{1}{5}}=\frac{-\frac{b}{30}+\frac{11}{12}}{\frac{1}{5}}$$

Dividing by \frac{1}{5} undoes the multiplication by \frac{1}{5}.

$$x=\frac{-\frac{b}{30}+\frac{11}{12}}{\frac{1}{5}}$$

Divide -\frac{b}{30}+\frac{11}{12} by \frac{1}{5} by multiplying -\frac{b}{30}+\frac{11}{12} by the reciprocal of \frac{1}{5}.

$$x=-\frac{b}{6}+\frac{55}{12}$$