Solve 2x+48+72=7/n+16

$$2 x + 48 + 72 = \frac { 7 } { n + 16 }$$

Solve for n

$$n=-\frac{32x+1913}{2\left(x+60\right)}$$

$$x\neq -60$$

Steps for Solving Linear Equation

Variable n cannot be equal to -16 since division by zero is not defined. Multiply both sides of the equation by n+16.

$$2x\left(n+16\right)+\left(n+16\right)\times 48+\left(n+16\right)\times 72=7$$

Use the distributive property to multiply 2x by n+16.

$$2xn+32x+\left(n+16\right)\times 48+\left(n+16\right)\times 72=7$$

Use the distributive property to multiply n+16 by 48.

$$2xn+32x+48n+768+\left(n+16\right)\times 72=7$$

Use the distributive property to multiply n+16 by 72.

$$2xn+32x+48n+768+72n+1152=7$$

Combine 48n and 72n to get 120n.

$$2xn+32x+120n+768+1152=7$$

Add 768 and 1152 to get 1920.

$$2xn+32x+120n+1920=7$$

Subtract 32x from both sides.

$$2xn+120n+1920=7-32x$$

Subtract 1920 from both sides.

$$2xn+120n=7-32x-1920$$

Subtract 1920 from 7 to get -1913.

$$2xn+120n=-1913-32x$$

Combine all terms containing n.

$$\left(2x+120\right)n=-1913-32x$$

The equation is in standard form.

$$\left(2x+120\right)n=-32x-1913$$

Divide both sides by 2x+120.

$$\frac{\left(2x+120\right)n}{2x+120}=\frac{-32x-1913}{2x+120}$$

Dividing by 2x+120 undoes the multiplication by 2x+120.

$$n=\frac{-32x-1913}{2x+120}$$

Divide -1913-32x by 2x+120.

$$n=-\frac{32x+1913}{2\left(x+60\right)}$$

Variable n cannot be equal to -16.

$$n=-\frac{32x+1913}{2\left(x+60\right)}\text{, }n\neq -16$$

Solve for x

$$x=-\frac{120n+1913}{2\left(n+16\right)}$$

$$n\neq -16$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n+16.

$$2x\left(n+16\right)+\left(n+16\right)\times 48+\left(n+16\right)\times 72=7$$

Use the distributive property to multiply 2x by n+16.

$$2xn+32x+\left(n+16\right)\times 48+\left(n+16\right)\times 72=7$$

Use the distributive property to multiply n+16 by 48.

$$2xn+32x+48n+768+\left(n+16\right)\times 72=7$$

Use the distributive property to multiply n+16 by 72.

$$2xn+32x+48n+768+72n+1152=7$$

Combine 48n and 72n to get 120n.

$$2xn+32x+120n+768+1152=7$$

Add 768 and 1152 to get 1920.

$$2xn+32x+120n+1920=7$$

Subtract 120n from both sides.

$$2xn+32x+1920=7-120n$$

Subtract 1920 from both sides.

$$2xn+32x=7-120n-1920$$

Subtract 1920 from 7 to get -1913.

$$2xn+32x=-1913-120n$$

Combine all terms containing x.

$$\left(2n+32\right)x=-1913-120n$$

The equation is in standard form.

$$\left(2n+32\right)x=-120n-1913$$

Divide both sides by 2n+32.

$$\frac{\left(2n+32\right)x}{2n+32}=\frac{-120n-1913}{2n+32}$$

Dividing by 2n+32 undoes the multiplication by 2n+32.

$$x=\frac{-120n-1913}{2n+32}$$

Divide -1913-120n by 2n+32.

$$x=-\frac{120n+1913}{2\left(n+16\right)}$$