Solve 2.5+x/x=5.8/5.2

$$\frac{ 2.5+x }{ x } = \frac{ 5.8 }{ 5.2 }$$

Solve for x

$$x = \frac{65}{3} = 21\frac{2}{3} \approx 21.666666667$$

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.

$$2.5+x=x\times \frac{5.8}{5.2}$$

Expand \frac{5.8}{5.2} by multiplying both numerator and the denominator by 10.

$$2.5+x=x\times \frac{58}{52}$$

Reduce the fraction \frac{58}{52} to lowest terms by extracting and canceling out 2.

$$2.5+x=x\times \frac{29}{26}$$

Subtract x\times \frac{29}{26} from both sides.

$$2.5+x-x\times \frac{29}{26}=0$$

Combine x and -x\times \frac{29}{26} to get -\frac{3}{26}x.

$$2.5-\frac{3}{26}x=0$$

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

$$-\frac{3}{26}x=-2.5$$

Multiply both sides by -\frac{26}{3}, the reciprocal of -\frac{3}{26}.

$$x=-2.5\left(-\frac{26}{3}\right)$$

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.

$$x=-\frac{5}{2}\left(-\frac{26}{3}\right)$$

Multiply -\frac{5}{2} times -\frac{26}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\left(-26\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{-5\left(-26\right)}{2\times 3}.

$$x=\frac{130}{6}$$

Reduce the fraction \frac{130}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{65}{3}$$