Solve b*1/3x-(x+1)=1/4x+1/2

$$b \cdot \frac { 1 } { 3 } x - ( x + 1 ) = \frac { 1 } { 4 } x + \frac { 1 } { 2 }$$

Solve for b

$$b=\frac{15}{4}+\frac{9}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

To find the opposite of x+1, find the opposite of each term.

$$b\times \frac{1}{3}x-x-1=\frac{1}{4}x+\frac{1}{2}$$

Add x to both sides.

$$b\times \frac{1}{3}x-1=\frac{1}{4}x+\frac{1}{2}+x$$

Combine \frac{1}{4}x and x to get \frac{5}{4}x.

$$b\times \frac{1}{3}x-1=\frac{5}{4}x+\frac{1}{2}$$

Add 1 to both sides.

$$b\times \frac{1}{3}x=\frac{5}{4}x+\frac{1}{2}+1$$

Add \frac{1}{2} and 1 to get \frac{3}{2}.

$$b\times \frac{1}{3}x=\frac{5}{4}x+\frac{3}{2}$$

The equation is in standard form.

$$\frac{x}{3}b=\frac{5x}{4}+\frac{3}{2}$$

Divide both sides by \frac{1}{3}x.

$$\frac{3\times \frac{x}{3}b}{x}=\frac{3\left(\frac{5x}{4}+\frac{3}{2}\right)}{x}$$

Dividing by \frac{1}{3}x undoes the multiplication by \frac{1}{3}x.

$$b=\frac{3\left(\frac{5x}{4}+\frac{3}{2}\right)}{x}$$

Divide \frac{5x}{4}+\frac{3}{2} by \frac{1}{3}x.

$$b=\frac{15}{4}+\frac{9}{2x}$$

Solve for x

$$x=\frac{18}{4b-15}$$

$$b\neq \frac{15}{4}$$

Steps for Solving Linear Equation

To find the opposite of x+1, find the opposite of each term.

$$b\times \frac{1}{3}x-x-1=\frac{1}{4}x+\frac{1}{2}$$

Subtract \frac{1}{4}x from both sides.

$$b\times \frac{1}{3}x-x-1-\frac{1}{4}x=\frac{1}{2}$$

Combine -x and -\frac{1}{4}x to get -\frac{5}{4}x.

$$b\times \frac{1}{3}x-\frac{5}{4}x-1=\frac{1}{2}$$

Add 1 to both sides.

$$b\times \frac{1}{3}x-\frac{5}{4}x=\frac{1}{2}+1$$

Add \frac{1}{2} and 1 to get \frac{3}{2}.

$$b\times \frac{1}{3}x-\frac{5}{4}x=\frac{3}{2}$$

Combine all terms containing x.

$$\left(b\times \frac{1}{3}-\frac{5}{4}\right)x=\frac{3}{2}$$

The equation is in standard form.

$$\left(\frac{b}{3}-\frac{5}{4}\right)x=\frac{3}{2}$$

Divide both sides by \frac{1}{3}b-\frac{5}{4}.

$$\frac{\left(\frac{b}{3}-\frac{5}{4}\right)x}{\frac{b}{3}-\frac{5}{4}}=\frac{\frac{3}{2}}{\frac{b}{3}-\frac{5}{4}}$$

Dividing by \frac{1}{3}b-\frac{5}{4} undoes the multiplication by \frac{1}{3}b-\frac{5}{4}.

$$x=\frac{\frac{3}{2}}{\frac{b}{3}-\frac{5}{4}}$$

Divide \frac{3}{2} by \frac{1}{3}b-\frac{5}{4}.

$$x=\frac{18}{4b-15}$$