Solve 1/10+x+1/100=2

$$\frac{ 1 }{ 10+x } + \frac{ 1 }{ 100 } =2$$

Solve for x

$$x = -\frac{1890}{199} = -9\frac{99}{199} \approx -9.497487437$$

Steps for Solving Linear Equation

Variable x cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by 100\left(x+10\right), the least common multiple of 10+x,100.

$$100+100\left(x+10\right)\times \frac{1}{100}=200\left(x+10\right)$$

Multiply 100 and \frac{1}{100} to get 1.

$$100+x+10=200\left(x+10\right)$$

Add 100 and 10 to get 110.

$$110+x=200\left(x+10\right)$$

Use the distributive property to multiply 200 by x+10.

$$110+x=200x+2000$$

Subtract 200x from both sides.

$$110+x-200x=2000$$

Combine x and -200x to get -199x.

$$110-199x=2000$$

Subtract 110 from both sides.

$$-199x=2000-110$$

Subtract 110 from 2000 to get 1890.

$$-199x=1890$$

Divide both sides by -199.

$$x=\frac{1890}{-199}$$

Fraction \frac{1890}{-199} can be rewritten as -\frac{1890}{199} by extracting the negative sign.

$$x=-\frac{1890}{199}$$