Solve 1/99x+1/99+3=2x+2+691/99

$$\frac{ 1 }{ 99 } x+ \frac{ 1 }{ 99 } +3=2x+2+ \frac{ 691 }{ 99 }$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Convert 3 to fraction \frac{297}{99}.

$$\frac{1}{99}x+\frac{1}{99}+\frac{297}{99}=2x+2+\frac{691}{99}$$

Since \frac{1}{99} and \frac{297}{99} have the same denominator, add them by adding their numerators.

$$\frac{1}{99}x+\frac{1+297}{99}=2x+2+\frac{691}{99}$$

Add 1 and 297 to get 298.

$$\frac{1}{99}x+\frac{298}{99}=2x+2+\frac{691}{99}$$

Convert 2 to fraction \frac{198}{99}.

$$\frac{1}{99}x+\frac{298}{99}=2x+\frac{198}{99}+\frac{691}{99}$$

Since \frac{198}{99} and \frac{691}{99} have the same denominator, add them by adding their numerators.

$$\frac{1}{99}x+\frac{298}{99}=2x+\frac{198+691}{99}$$

Add 198 and 691 to get 889.

$$\frac{1}{99}x+\frac{298}{99}=2x+\frac{889}{99}$$

Subtract 2x from both sides.

$$\frac{1}{99}x+\frac{298}{99}-2x=\frac{889}{99}$$

Combine \frac{1}{99}x and -2x to get -\frac{197}{99}x.

$$-\frac{197}{99}x+\frac{298}{99}=\frac{889}{99}$$

Subtract \frac{298}{99} from both sides.

$$-\frac{197}{99}x=\frac{889}{99}-\frac{298}{99}$$

Since \frac{889}{99} and \frac{298}{99} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{197}{99}x=\frac{889-298}{99}$$

Subtract 298 from 889 to get 591.

$$-\frac{197}{99}x=\frac{591}{99}$$

Reduce the fraction \frac{591}{99} to lowest terms by extracting and canceling out 3.

$$-\frac{197}{99}x=\frac{197}{33}$$

Multiply both sides by -\frac{99}{197}, the reciprocal of -\frac{197}{99}.

$$x=\frac{197}{33}\left(-\frac{99}{197}\right)$$

Multiply \frac{197}{33} times -\frac{99}{197} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{197\left(-99\right)}{33\times 197}$$

Cancel out 197 in both numerator and denominator.

$$x=\frac{-99}{33}$$

Divide -99 by 33 to get -3.

$$x=-3$$