Solve 6/7.5=2x/2x+32

$$\frac{ 6 }{ 7.5 } = \frac{ 2x }{ 2x+32 }$$

Solve for x

$$x=64$$

Steps for Solving Linear Equation

Variable x cannot be equal to -16 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+16\right).

$$2\left(x+16\right)\times \frac{6}{7.5}=2x$$

Use the distributive property to multiply 2 by x+16.

$$\left(2x+32\right)\times \frac{6}{7.5}=2x$$

Expand \frac{6}{7.5} by multiplying both numerator and the denominator by 10.

$$\left(2x+32\right)\times \frac{60}{75}=2x$$

Reduce the fraction \frac{60}{75} to lowest terms by extracting and canceling out 15.

$$\left(2x+32\right)\times \frac{4}{5}=2x$$

Use the distributive property to multiply 2x+32 by \frac{4}{5}.

$$\frac{8}{5}x+\frac{128}{5}=2x$$

Subtract 2x from both sides.

$$\frac{8}{5}x+\frac{128}{5}-2x=0$$

Combine \frac{8}{5}x and -2x to get -\frac{2}{5}x.

$$-\frac{2}{5}x+\frac{128}{5}=0$$

Subtract \frac{128}{5} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{2}{5}x=-\frac{128}{5}$$

Multiply both sides by -\frac{5}{2}, the reciprocal of -\frac{2}{5}.

$$x=-\frac{128}{5}\left(-\frac{5}{2}\right)$$

Multiply -\frac{128}{5} and -\frac{5}{2} to get 64.

$$x=64$$