Solve g10/x+1/5x=19/10

$$g \frac { 10 } { x } + \frac { 1 } { 5 x } = \frac { 19 } { 10 }$$

Solve for g

$$g=\frac{19x}{100}-\frac{1}{50}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10x, the least common multiple of x,5x,10.

$$g\times 10\times 10+2=19x$$

Multiply 10 and 10 to get 100.

$$g\times 100+2=19x$$

Subtract 2 from both sides.

$$g\times 100=19x-2$$

The equation is in standard form.

$$100g=19x-2$$

Divide both sides by 100.

$$\frac{100g}{100}=\frac{19x-2}{100}$$

Dividing by 100 undoes the multiplication by 100.

$$g=\frac{19x-2}{100}$$

Divide 19x-2 by 100.

$$g=\frac{19x}{100}-\frac{1}{50}$$

Solve for x

$$x=\frac{100g+2}{19}$$

$$g\neq -\frac{1}{50}$$

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 10x, the least common multiple of x,5x,10.

$$g\times 10\times 10+2=19x$$

Multiply 10 and 10 to get 100.

$$g\times 100+2=19x$$

Swap sides so that all variable terms are on the left hand side.

$$19x=g\times 100+2$$

The equation is in standard form.

$$19x=100g+2$$

Divide both sides by 19.

$$\frac{19x}{19}=\frac{100g+2}{19}$$

Dividing by 19 undoes the multiplication by 19.

$$x=\frac{100g+2}{19}$$

Variable x cannot be equal to 0.

$$x=\frac{100g+2}{19}\text{, }x\neq 0$$