Solve x+25/5+x=5/2/frac{16{5}}

$$\frac { x + 25 } { 5 + x } = \frac { \frac { 5 } { 2 } } { \frac { 16 } { 5 } }$$

Solve for x

$$x = -\frac{675}{7} = -96\frac{3}{7} \approx -96.428571429$$

Steps for Solving Linear Equation

Variable x cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by x+5.

$$x+25=\left(x+5\right)\times \frac{\frac{5}{2}}{\frac{16}{5}}$$

Divide \frac{5}{2} by \frac{16}{5} by multiplying \frac{5}{2} by the reciprocal of \frac{16}{5}.

$$x+25=\left(x+5\right)\times \frac{5}{2}\times \frac{5}{16}$$

Multiply \frac{5}{2} and \frac{5}{16} to get \frac{25}{32}.

$$x+25=\left(x+5\right)\times \frac{25}{32}$$

Use the distributive property to multiply x+5 by \frac{25}{32}.

$$x+25=\frac{25}{32}x+\frac{125}{32}$$

Subtract \frac{25}{32}x from both sides.

$$x+25-\frac{25}{32}x=\frac{125}{32}$$

Combine x and -\frac{25}{32}x to get \frac{7}{32}x.

$$\frac{7}{32}x+25=\frac{125}{32}$$

Subtract 25 from both sides.

$$\frac{7}{32}x=\frac{125}{32}-25$$

Subtract 25 from \frac{125}{32} to get -\frac{675}{32}.

$$\frac{7}{32}x=-\frac{675}{32}$$

Multiply both sides by \frac{32}{7}, the reciprocal of \frac{7}{32}.

$$x=-\frac{675}{32}\times \frac{32}{7}$$

Multiply -\frac{675}{32} and \frac{32}{7} to get -\frac{675}{7}.

$$x=-\frac{675}{7}$$