Solve a/x+b/2=4a/x

$$\frac { a } { x } + \frac { b } { 2 } = \frac { 4 a } { x }$$

Solve for a

$$a=\frac{bx}{6}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x, the least common multiple of x,2.

$$2a+xb=2\times 4a$$

Multiply 2 and 4 to get 8.

$$2a+xb=8a$$

Subtract 8a from both sides.

$$2a+xb-8a=0$$

Combine 2a and -8a to get -6a.

$$-6a+xb=0$$

Subtract xb from both sides. Anything subtracted from zero gives its negation.

$$-6a=-xb$$

Reorder the terms.

$$-6a=-bx$$

Divide both sides by -6.

$$\frac{-6a}{-6}=-\frac{bx}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$a=-\frac{bx}{-6}$$

Divide -bx by -6.

$$a=\frac{bx}{6}$$

Solve for b

$$b=\frac{6a}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x, the least common multiple of x,2.

$$2a+xb=2\times 4a$$

Multiply 2 and 4 to get 8.

$$2a+xb=8a$$

Subtract 2a from both sides.

$$xb=8a-2a$$

Combine 8a and -2a to get 6a.

$$xb=6a$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{6a}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{6a}{x}$$