Solve 1/x-15/-300=-0.5/-200

$$\frac { 1 } { x } - \frac { 15 } { - 300 } = \frac { - 0.5 } { - 200 }$$

Solve for x

$$x = -\frac{400}{19} = -21\frac{1}{19} \approx -21.052631579$$

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 600x, the least common multiple of x,-300,-200.

$$600-\left(-2x\times 15\right)=-3x\left(-0.5\right)$$

Multiply -2 and 15 to get -30.

$$600-\left(-30x\right)=-3x\left(-0.5\right)$$

The opposite of -30x is 30x.

$$600+30x=-3x\left(-0.5\right)$$

Multiply -3 and -0.5 to get 1.5.

$$600+30x=1.5x$$

Subtract 1.5x from both sides.

$$600+30x-1.5x=0$$

Combine 30x and -1.5x to get 28.5x.

$$600+28.5x=0$$

Subtract 600 from both sides. Anything subtracted from zero gives its negation.

$$28.5x=-600$$

Divide both sides by 28.5.

$$x=\frac{-600}{28.5}$$

Expand \frac{-600}{28.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{-6000}{285}$$

Reduce the fraction \frac{-6000}{285} to lowest terms by extracting and canceling out 15.

$$x=-\frac{400}{19}$$