Solve x-h+(x)/3-b-x/m=h

$$\frac { x - h + ( x ) } { 3 } - \frac { b - x } { m } = h$$

Solve for b

$$b=\frac{2mx}{3}-\frac{4hm}{3}+x$$

$$m\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3m, the least common multiple of 3,m.

$$m\left(x-h+x\right)-3\left(b-x\right)=h\times 3m$$

Combine x and x to get 2x.

$$m\left(2x-h\right)-3\left(b-x\right)=h\times 3m$$

Use the distributive property to multiply m by 2x-h.

$$2mx-mh-3\left(b-x\right)=h\times 3m$$

Use the distributive property to multiply -3 by b-x.

$$2mx-mh-3b+3x=h\times 3m$$

Subtract 2mx from both sides.

$$-mh-3b+3x=h\times 3m-2mx$$

Add mh to both sides.

$$-3b+3x=h\times 3m-2mx+mh$$

Combine h\times 3m and mh to get 4hm.

$$-3b+3x=4hm-2mx$$

Subtract 3x from both sides.

$$-3b=4hm-2mx-3x$$

The equation is in standard form.

$$-3b=4hm-3x-2mx$$

Divide both sides by -3.

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

Dividing by -3 undoes the multiplication by -3.

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

Divide 4hm-2mx-3x by -3.

$$b=\frac{2mx}{3}-\frac{4hm}{3}+x$$

Solve for h

$$h=\frac{2mx+3x-3b}{4m}$$

$$m\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3m, the least common multiple of 3,m.

$$m\left(x-h+x\right)-3\left(b-x\right)=h\times 3m$$

Combine x and x to get 2x.

$$m\left(2x-h\right)-3\left(b-x\right)=h\times 3m$$

Use the distributive property to multiply m by 2x-h.

$$2mx-mh-3\left(b-x\right)=h\times 3m$$

Use the distributive property to multiply -3 by b-x.

$$2mx-mh-3b+3x=h\times 3m$$

Subtract h\times 3m from both sides.

$$2mx-mh-3b+3x-h\times 3m=0$$

Combine -mh and -h\times 3m to get -4mh.

$$2mx-4mh-3b+3x=0$$

Subtract 2mx from both sides. Anything subtracted from zero gives its negation.

$$-4mh-3b+3x=-2mx$$

Add 3b to both sides.

$$-4mh+3x=-2mx+3b$$

Subtract 3x from both sides.

$$-4mh=-2mx+3b-3x$$

The equation is in standard form.

$$\left(-4m\right)h=3b-3x-2mx$$

Divide both sides by -4m.

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

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

$$h=\frac{3b-3x-2mx}{-4m}$$

Divide -2mx+3b-3x by -4m.

$$h=-\frac{3b-3x-2mx}{4m}$$