Solve 2.5+x/x=5.8/3.2

$$\frac{ 2.5+x }{ x } = \frac{ 5.8 }{ 3.2 }$$

Solve for x

$$x = \frac{40}{13} = 3\frac{1}{13} \approx 3.076923077$$

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 x.

$$2.5+x=x\times \frac{5.8}{3.2}$$

Expand \frac{5.8}{3.2} by multiplying both numerator and the denominator by 10.

$$2.5+x=x\times \frac{58}{32}$$

Reduce the fraction \frac{58}{32} to lowest terms by extracting and canceling out 2.

$$2.5+x=x\times \frac{29}{16}$$

Subtract x\times \frac{29}{16} from both sides.

$$2.5+x-x\times \frac{29}{16}=0$$

Combine x and -x\times \frac{29}{16} to get -\frac{13}{16}x.

$$2.5-\frac{13}{16}x=0$$

Subtract 2.5 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{13}{16}x=-2.5$$

Multiply both sides by -\frac{16}{13}, the reciprocal of -\frac{13}{16}.

$$x=-2.5\left(-\frac{16}{13}\right)$$

Convert decimal number -2.5 to fraction -\frac{25}{10}. Reduce the fraction -\frac{25}{10} to lowest terms by extracting and canceling out 5.

$$x=-\frac{5}{2}\left(-\frac{16}{13}\right)$$

Multiply -\frac{5}{2} times -\frac{16}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\left(-16\right)}{2\times 13}$$

Do the multiplications in the fraction \frac{-5\left(-16\right)}{2\times 13}.

$$x=\frac{80}{26}$$

Reduce the fraction \frac{80}{26} to lowest terms by extracting and canceling out 2.

$$x=\frac{40}{13}$$