Solve 11/9x+4/7(1000-x)=999

$$\frac { 11 } { 9 } x + \frac { 4 } { 7 } ( 1000 - x ) = 999$$

Solve for x

$$x=657$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{7} by 1000-x.

$$\frac{11}{9}x+\frac{4}{7}\times 1000+\frac{4}{7}\left(-1\right)x=999$$

Express \frac{4}{7}\times 1000 as a single fraction.

$$\frac{11}{9}x+\frac{4\times 1000}{7}+\frac{4}{7}\left(-1\right)x=999$$

Multiply 4 and 1000 to get 4000.

$$\frac{11}{9}x+\frac{4000}{7}+\frac{4}{7}\left(-1\right)x=999$$

Multiply \frac{4}{7} and -1 to get -\frac{4}{7}.

$$\frac{11}{9}x+\frac{4000}{7}-\frac{4}{7}x=999$$

Combine \frac{11}{9}x and -\frac{4}{7}x to get \frac{41}{63}x.

$$\frac{41}{63}x+\frac{4000}{7}=999$$

Subtract \frac{4000}{7} from both sides.

$$\frac{41}{63}x=999-\frac{4000}{7}$$

Convert 999 to fraction \frac{6993}{7}.

$$\frac{41}{63}x=\frac{6993}{7}-\frac{4000}{7}$$

Since \frac{6993}{7} and \frac{4000}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41}{63}x=\frac{6993-4000}{7}$$

Subtract 4000 from 6993 to get 2993.

$$\frac{41}{63}x=\frac{2993}{7}$$

Multiply both sides by \frac{63}{41}, the reciprocal of \frac{41}{63}.

$$x=\frac{2993}{7}\times \frac{63}{41}$$

Multiply \frac{2993}{7} times \frac{63}{41} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{2993\times 63}{7\times 41}$$

Do the multiplications in the fraction \frac{2993\times 63}{7\times 41}.

$$x=\frac{188559}{287}$$

Divide 188559 by 287 to get 657.

$$x=657$$