Solve (a-1)x/6-1=x/2

$$\frac { ( a - 1 ) x } { 6 } - 1 = \frac { x } { 2 }$$

Solve for a

$$a=4+\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 6,2.

$$\left(a-1\right)x-6=3x$$

Use the distributive property to multiply a-1 by x.

$$ax-x-6=3x$$

Add x to both sides.

$$ax-6=3x+x$$

Combine 3x and x to get 4x.

$$ax-6=4x$$

Add 6 to both sides.

$$ax=4x+6$$

The equation is in standard form.

$$xa=4x+6$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{4x+6}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{4x+6}{x}$$

Divide 4x+6 by x.

$$a=4+\frac{6}{x}$$

Solve for x

$$x=\frac{6}{a-4}$$

$$a\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 6,2.

$$\left(a-1\right)x-6=3x$$

Use the distributive property to multiply a-1 by x.

$$ax-x-6=3x$$

Subtract 3x from both sides.

$$ax-x-6-3x=0$$

Combine -x and -3x to get -4x.

$$ax-4x-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$ax-4x=6$$

Combine all terms containing x.

$$\left(a-4\right)x=6$$

Divide both sides by a-4.

$$\frac{\left(a-4\right)x}{a-4}=\frac{6}{a-4}$$

Dividing by a-4 undoes the multiplication by a-4.

$$x=\frac{6}{a-4}$$