Solve 1.5*500/x=100/x+5

$$1.5 \cdot \frac { 500 } { x } = \frac { 100 } { x + 5 }$$

Solve for x

$$x = -\frac{75}{13} = -5\frac{10}{13} \approx -5.769230769$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+5\right), the least common multiple of x,x+5.

$$1.5\left(x+5\right)\times 500=x\times 100$$

Multiply 1.5 and 500 to get 750.

$$750\left(x+5\right)=x\times 100$$

Use the distributive property to multiply 750 by x+5.

$$750x+3750=x\times 100$$

Subtract x\times 100 from both sides.

$$750x+3750-x\times 100=0$$

Combine 750x and -x\times 100 to get 650x.

$$650x+3750=0$$

Subtract 3750 from both sides. Anything subtracted from zero gives its negation.

$$650x=-3750$$

Divide both sides by 650.

$$x=\frac{-3750}{650}$$

Reduce the fraction \frac{-3750}{650} to lowest terms by extracting and canceling out 50.

$$x=-\frac{75}{13}$$