Solve -2/1.059-0.653=6-x/0.059

$$\frac { - 2 } { 1.059 - 0.653 } = \frac { 6 - x } { 0.059 }$$

Solve for x

$$x = \frac{1277}{203} = 6\frac{59}{203} \approx 6.290640394$$

Steps for Solving Linear Equation

Subtract 0.653 from 1.059 to get 0.406.

$$\frac{-2}{0.406}=\frac{6-x}{0.059}$$

Expand \frac{-2}{0.406} by multiplying both numerator and the denominator by 1000.

$$\frac{-2000}{406}=\frac{6-x}{0.059}$$

Reduce the fraction \frac{-2000}{406} to lowest terms by extracting and canceling out 2.

$$-\frac{1000}{203}=\frac{6-x}{0.059}$$

Divide each term of 6-x by 0.059 to get \frac{6}{0.059}+\frac{-x}{0.059}.

$$-\frac{1000}{203}=\frac{6}{0.059}+\frac{-x}{0.059}$$

Expand \frac{6}{0.059} by multiplying both numerator and the denominator by 1000.

$$-\frac{1000}{203}=\frac{6000}{59}+\frac{-x}{0.059}$$

Divide -x by 0.059 to get -\frac{1000}{59}x.

$$-\frac{1000}{203}=\frac{6000}{59}-\frac{1000}{59}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{6000}{59}-\frac{1000}{59}x=-\frac{1000}{203}$$

Subtract \frac{6000}{59} from both sides.

$$-\frac{1000}{59}x=-\frac{1000}{203}-\frac{6000}{59}$$

Least common multiple of 203 and 59 is 11977. Convert -\frac{1000}{203} and \frac{6000}{59} to fractions with denominator 11977.

$$-\frac{1000}{59}x=-\frac{59000}{11977}-\frac{1218000}{11977}$$

Since -\frac{59000}{11977} and \frac{1218000}{11977} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1000}{59}x=\frac{-59000-1218000}{11977}$$

Subtract 1218000 from -59000 to get -1277000.

$$-\frac{1000}{59}x=-\frac{1277000}{11977}$$

Divide both sides by -\frac{1000}{59}.

$$x=\frac{-\frac{1277000}{11977}}{-\frac{1000}{59}}$$

Express \frac{-\frac{1277000}{11977}}{-\frac{1000}{59}} as a single fraction.

$$x=\frac{-1277000}{11977\left(-\frac{1000}{59}\right)}$$

Multiply 11977 and -\frac{1000}{59} to get -203000.

$$x=\frac{-1277000}{-203000}$$

Reduce the fraction \frac{-1277000}{-203000} to lowest terms by extracting and canceling out -1000.

$$x=\frac{1277}{203}$$