Solve n/9*+4/7(1000-x)=999

$$\frac { n } { 9 } \times + \frac { 4 } { 7 } ( 1000 - x ) = 999$$

Solve for n

$$n=\frac{62937}{4\left(1000-x\right)}$$

$$x\neq 1000$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 63, the least common multiple of 9,7.

$$7n\times \frac{4}{7}\left(1000-x\right)=62937$$

Multiply 7 and \frac{4}{7} to get 4.

$$4n\left(1000-x\right)=62937$$

Use the distributive property to multiply 4n by 1000-x.

$$4000n-4nx=62937$$

Combine all terms containing n.

$$\left(4000-4x\right)n=62937$$

Divide both sides by -4x+4000.

$$\frac{\left(4000-4x\right)n}{4000-4x}=\frac{62937}{4000-4x}$$

Dividing by -4x+4000 undoes the multiplication by -4x+4000.

$$n=\frac{62937}{4000-4x}$$

Divide 62937 by -4x+4000.

$$n=\frac{62937}{4\left(1000-x\right)}$$

Solve for x

$$x=1000-\frac{62937}{4n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 63, the least common multiple of 9,7.

$$7n\times \frac{4}{7}\left(1000-x\right)=62937$$

Multiply 7 and \frac{4}{7} to get 4.

$$4n\left(1000-x\right)=62937$$

Use the distributive property to multiply 4n by 1000-x.

$$4000n-4xn=62937$$

Subtract 4000n from both sides.

$$-4xn=62937-4000n$$

The equation is in standard form.

$$\left(-4n\right)x=62937-4000n$$

Divide both sides by -4n.

$$\frac{\left(-4n\right)x}{-4n}=\frac{62937-4000n}{-4n}$$

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

$$x=\frac{62937-4000n}{-4n}$$

Divide 62937-4000n by -4n.

$$x=1000-\frac{62937}{4n}$$