Solve 685/33+(x-1)-83/33=13

$$\frac{ 685 }{ 33 } +(x-1) \frac{ -83 }{ 33 } =13$$

Solve for x

$$x = \frac{339}{83} = 4\frac{7}{83} \approx 4.084337349$$

Steps for Solving Linear Equation

Fraction \frac{-83}{33} can be rewritten as -\frac{83}{33} by extracting the negative sign.

$$\frac{685}{33}+\left(x-1\right)\left(-\frac{83}{33}\right)=13$$

Use the distributive property to multiply x-1 by -\frac{83}{33}.

$$\frac{685}{33}+x\left(-\frac{83}{33}\right)-\left(-\frac{83}{33}\right)=13$$

Multiply -1 and -\frac{83}{33} to get \frac{83}{33}.

$$\frac{685}{33}+x\left(-\frac{83}{33}\right)+\frac{83}{33}=13$$

Since \frac{685}{33} and \frac{83}{33} have the same denominator, add them by adding their numerators.

$$\frac{685+83}{33}+x\left(-\frac{83}{33}\right)=13$$

Add 685 and 83 to get 768.

$$\frac{768}{33}+x\left(-\frac{83}{33}\right)=13$$

Reduce the fraction \frac{768}{33} to lowest terms by extracting and canceling out 3.

$$\frac{256}{11}+x\left(-\frac{83}{33}\right)=13$$

Subtract \frac{256}{11} from both sides.

$$x\left(-\frac{83}{33}\right)=13-\frac{256}{11}$$

Convert 13 to fraction \frac{143}{11}.

$$x\left(-\frac{83}{33}\right)=\frac{143}{11}-\frac{256}{11}$$

Since \frac{143}{11} and \frac{256}{11} have the same denominator, subtract them by subtracting their numerators.

$$x\left(-\frac{83}{33}\right)=\frac{143-256}{11}$$

Subtract 256 from 143 to get -113.

$$x\left(-\frac{83}{33}\right)=-\frac{113}{11}$$

Multiply both sides by -\frac{33}{83}, the reciprocal of -\frac{83}{33}.

$$x=-\frac{113}{11}\left(-\frac{33}{83}\right)$$

Multiply -\frac{113}{11} times -\frac{33}{83} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-113\left(-33\right)}{11\times 83}$$

Do the multiplications in the fraction \frac{-113\left(-33\right)}{11\times 83}.

$$x=\frac{3729}{913}$$

Reduce the fraction \frac{3729}{913} to lowest terms by extracting and canceling out 11.

$$x=\frac{339}{83}$$