Solve 1.56/613+1/x=1-1.56/-115

$$\frac { 1.56 } { 613 } + \frac { 1 } { x } = \frac { 1 - 1.56 } { - 115 }$$

Solve for x

$$x = \frac{1762375}{4097} = 430\frac{665}{4097} \approx 430.162313888$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 70495x, the least common multiple of 613,x,-115.

$$115x\times 1.56+70495=-613x\left(1-1.56\right)$$

Multiply 115 and 1.56 to get 179.4.

$$179.4x+70495=-613x\left(1-1.56\right)$$

Subtract 1.56 from 1 to get -0.56.

$$179.4x+70495=-613x\left(-0.56\right)$$

Multiply -613 and -0.56 to get 343.28.

$$179.4x+70495=343.28x$$

Subtract 343.28x from both sides.

$$179.4x+70495-343.28x=0$$

Combine 179.4x and -343.28x to get -163.88x.

$$-163.88x+70495=0$$

Subtract 70495 from both sides. Anything subtracted from zero gives its negation.

$$-163.88x=-70495$$

Divide both sides by -163.88.

$$x=\frac{-70495}{-163.88}$$

Expand \frac{-70495}{-163.88} by multiplying both numerator and the denominator by 100.

$$x=\frac{-7049500}{-16388}$$

Reduce the fraction \frac{-7049500}{-16388} to lowest terms by extracting and canceling out -4.

$$x=\frac{1762375}{4097}$$