Solve 2/5x=5/11(x+5)

$$\frac { 2 } { 5 } x = \frac { 5 } { 11 } ( x + 5 )$$

Solve for x

$$x = -\frac{125}{3} = -41\frac{2}{3} \approx -41.666666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{11} by x+5.

$$\frac{2}{5}x=\frac{5}{11}x+\frac{5}{11}\times 5$$

Express \frac{5}{11}\times 5 as a single fraction.

$$\frac{2}{5}x=\frac{5}{11}x+\frac{5\times 5}{11}$$

Multiply 5 and 5 to get 25.

$$\frac{2}{5}x=\frac{5}{11}x+\frac{25}{11}$$

Subtract \frac{5}{11}x from both sides.

$$\frac{2}{5}x-\frac{5}{11}x=\frac{25}{11}$$

Combine \frac{2}{5}x and -\frac{5}{11}x to get -\frac{3}{55}x.

$$-\frac{3}{55}x=\frac{25}{11}$$

Multiply both sides by -\frac{55}{3}, the reciprocal of -\frac{3}{55}.

$$x=\frac{25}{11}\left(-\frac{55}{3}\right)$$

Multiply \frac{25}{11} times -\frac{55}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{25\left(-55\right)}{11\times 3}$$

Do the multiplications in the fraction \frac{25\left(-55\right)}{11\times 3}.

$$x=\frac{-1375}{33}$$

Reduce the fraction \frac{-1375}{33} to lowest terms by extracting and canceling out 11.

$$x=-\frac{125}{3}$$