Solve 6x-h/2=7hx+1/3

$$\frac { 6 x - h } { 2 } = \frac { 7 h x + 1 } { 3 }$$

Solve for h

$$h=\frac{2\left(9x-1\right)}{14x+3}$$

$$x\neq -\frac{3}{14}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(6x-h\right)=2\left(7hx+1\right)$$

Use the distributive property to multiply 3 by 6x-h.

$$18x-3h=2\left(7hx+1\right)$$

Use the distributive property to multiply 2 by 7hx+1.

$$18x-3h=14xh+2$$

Subtract 14xh from both sides.

$$18x-3h-14xh=2$$

Subtract 18x from both sides.

$$-3h-14xh=2-18x$$

Combine all terms containing h.

$$\left(-3-14x\right)h=2-18x$$

The equation is in standard form.

$$\left(-14x-3\right)h=2-18x$$

Divide both sides by -3-14x.

$$\frac{\left(-14x-3\right)h}{-14x-3}=\frac{2-18x}{-14x-3}$$

Dividing by -3-14x undoes the multiplication by -3-14x.

$$h=\frac{2-18x}{-14x-3}$$

Divide 2-18x by -3-14x.

$$h=-\frac{2\left(1-9x\right)}{14x+3}$$

Solve for x

$$x=\frac{3h+2}{2\left(9-7h\right)}$$

$$h\neq \frac{9}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(6x-h\right)=2\left(7hx+1\right)$$

Use the distributive property to multiply 3 by 6x-h.

$$18x-3h=2\left(7hx+1\right)$$

Use the distributive property to multiply 2 by 7hx+1.

$$18x-3h=14hx+2$$

Subtract 14hx from both sides.

$$18x-3h-14hx=2$$

Add 3h to both sides.

$$18x-14hx=2+3h$$

Combine all terms containing x.

$$\left(18-14h\right)x=2+3h$$

The equation is in standard form.

$$\left(18-14h\right)x=3h+2$$

Divide both sides by 18-14h.

$$\frac{\left(18-14h\right)x}{18-14h}=\frac{3h+2}{18-14h}$$

Dividing by 18-14h undoes the multiplication by 18-14h.

$$x=\frac{3h+2}{18-14h}$$

Divide 2+3h by 18-14h.

$$x=\frac{3h+2}{2\left(9-7h\right)}$$