Solve 4-a=2/x-1

$$4 - a = \frac { 2 } { x - 1 }$$

Solve for a

$$a=-\frac{2\left(2x-3\right)}{1-x}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-1.

$$\left(x-1\right)\times 4-a\left(x-1\right)=2$$

Use the distributive property to multiply x-1 by 4.

$$4x-4-a\left(x-1\right)=2$$

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

$$4x-4-ax+a=2$$

Subtract 4x from both sides.

$$-4-ax+a=2-4x$$

Add 4 to both sides.

$$-ax+a=2-4x+4$$

Add 2 and 4 to get 6.

$$-ax+a=6-4x$$

Combine all terms containing a.

$$\left(-x+1\right)a=6-4x$$

The equation is in standard form.

$$\left(1-x\right)a=6-4x$$

Divide both sides by -x+1.

$$\frac{\left(1-x\right)a}{1-x}=\frac{6-4x}{1-x}$$

Dividing by -x+1 undoes the multiplication by -x+1.

$$a=\frac{6-4x}{1-x}$$

Divide 6-4x by -x+1.

$$a=\frac{2\left(3-2x\right)}{1-x}$$

Solve for x

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

$$a\neq 4$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$\left(x-1\right)\times 4-a\left(x-1\right)=2$$

Use the distributive property to multiply x-1 by 4.

$$4x-4-a\left(x-1\right)=2$$

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

$$4x-4-ax+a=2$$

Add 4 to both sides.

$$4x-ax+a=2+4$$

Add 2 and 4 to get 6.

$$4x-ax+a=6$$

Subtract a from both sides.

$$4x-ax=6-a$$

Combine all terms containing x.

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

Divide both sides by 4-a.

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

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

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

Variable x cannot be equal to 1.

$$x=\frac{6-a}{4-a}\text{, }x\neq 1$$