Solve 19+x/65+x*100=36

$$\frac { 19 + x } { 65 + x } \times 100 = 36$$

Solve for x

$$x = \frac{55}{8} = 6\frac{7}{8} = 6.875$$

Steps for Solving Linear Equation

Divide both sides by 100.

$$\frac{19+x}{65+x}=\frac{36}{100}$$

Reduce the fraction \frac{36}{100} to lowest terms by extracting and canceling out 4.

$$\frac{19+x}{65+x}=\frac{9}{25}$$

Variable x cannot be equal to -65 since division by zero is not defined. Multiply both sides of the equation by 25\left(x+65\right), the least common multiple of 65+x,25.

$$25\left(19+x\right)=9\left(x+65\right)$$

Use the distributive property to multiply 25 by 19+x.

$$475+25x=9\left(x+65\right)$$

Use the distributive property to multiply 9 by x+65.

$$475+25x=9x+585$$

Subtract 9x from both sides.

$$475+25x-9x=585$$

Combine 25x and -9x to get 16x.

$$475+16x=585$$

Subtract 475 from both sides.

$$16x=585-475$$

Subtract 475 from 585 to get 110.

$$16x=110$$

Divide both sides by 16.

$$x=\frac{110}{16}$$

Reduce the fraction \frac{110}{16} to lowest terms by extracting and canceling out 2.

$$x=\frac{55}{8}$$