Solve 1/h(-4)=1/2x-2

$$\frac { 1 } { h ( - 4 ) } = \frac { 1 } { 2 } x - 2$$

Solve for h

$$h=-\frac{1}{2\left(x-4\right)}$$

$$x\neq 4$$

Steps for Solving Linear Equation

Variable h cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4h, the least common multiple of h\left(-4\right),2.

$$-1=\frac{1}{2}x\times 4h+4h\left(-2\right)$$

Multiply \frac{1}{2} and 4 to get 2.

$$-1=2xh+4h\left(-2\right)$$

Multiply 4 and -2 to get -8.

$$-1=2xh-8h$$

Swap sides so that all variable terms are on the left hand side.

$$2xh-8h=-1$$

Combine all terms containing h.

$$\left(2x-8\right)h=-1$$

Divide both sides by 2x-8.

$$\frac{\left(2x-8\right)h}{2x-8}=-\frac{1}{2x-8}$$

Dividing by 2x-8 undoes the multiplication by 2x-8.

$$h=-\frac{1}{2x-8}$$

Divide -1 by 2x-8.

$$h=-\frac{1}{2\left(x-4\right)}$$

Variable h cannot be equal to 0.

$$h=-\frac{1}{2\left(x-4\right)}\text{, }h\neq 0$$

Solve for x

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

$$h\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4h, the least common multiple of h\left(-4\right),2.

$$-1=\frac{1}{2}x\times 4h+4h\left(-2\right)$$

Multiply \frac{1}{2} and 4 to get 2.

$$-1=2xh+4h\left(-2\right)$$

Multiply 4 and -2 to get -8.

$$-1=2xh-8h$$

Swap sides so that all variable terms are on the left hand side.

$$2xh-8h=-1$$

Add 8h to both sides.

$$2xh=-1+8h$$

The equation is in standard form.

$$2hx=8h-1$$

Divide both sides by 2h.

$$\frac{2hx}{2h}=\frac{8h-1}{2h}$$

Dividing by 2h undoes the multiplication by 2h.

$$x=\frac{8h-1}{2h}$$

Divide -1+8h by 2h.

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