Solve 250/2-250/x+25=1/2

$$\frac { 250 } { 2 } - \frac { 250 } { x + 25 } = \frac { 1 } { 2 }$$

Solve for x

$$x = -\frac{5725}{249} = -22\frac{247}{249} \approx -22.991967871$$

Steps for Solving Linear Equation

Variable x cannot be equal to -25 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+25\right), the least common multiple of 2,x+25.

$$\left(x+25\right)\times 250-2\times 250=x+25$$

Use the distributive property to multiply x+25 by 250.

$$250x+6250-2\times 250=x+25$$

Multiply -2 and 250 to get -500.

$$250x+6250-500=x+25$$

Subtract 500 from 6250 to get 5750.

$$250x+5750=x+25$$

Subtract x from both sides.

$$250x+5750-x=25$$

Combine 250x and -x to get 249x.

$$249x+5750=25$$

Subtract 5750 from both sides.

$$249x=25-5750$$

Subtract 5750 from 25 to get -5725.

$$249x=-5725$$

Divide both sides by 249.

$$x=\frac{-5725}{249}$$

Fraction \frac{-5725}{249} can be rewritten as -\frac{5725}{249} by extracting the negative sign.

$$x=-\frac{5725}{249}$$