Solve 1/3x+5=5/13(x+5)

$$\frac{ 1 }{ 3 } x+5= \frac{ 5 }{ 13 } (x+5)$$

Solve for x

$$x=60$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{13} by x+5.

$$\frac{1}{3}x+5=\frac{5}{13}x+\frac{5}{13}\times 5$$

Express \frac{5}{13}\times 5 as a single fraction.

$$\frac{1}{3}x+5=\frac{5}{13}x+\frac{5\times 5}{13}$$

Multiply 5 and 5 to get 25.

$$\frac{1}{3}x+5=\frac{5}{13}x+\frac{25}{13}$$

Subtract \frac{5}{13}x from both sides.

$$\frac{1}{3}x+5-\frac{5}{13}x=\frac{25}{13}$$

Combine \frac{1}{3}x and -\frac{5}{13}x to get -\frac{2}{39}x.

$$-\frac{2}{39}x+5=\frac{25}{13}$$

Subtract 5 from both sides.

$$-\frac{2}{39}x=\frac{25}{13}-5$$

Convert 5 to fraction \frac{65}{13}.

$$-\frac{2}{39}x=\frac{25}{13}-\frac{65}{13}$$

Since \frac{25}{13} and \frac{65}{13} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{39}x=\frac{25-65}{13}$$

Subtract 65 from 25 to get -40.

$$-\frac{2}{39}x=-\frac{40}{13}$$

Multiply both sides by -\frac{39}{2}, the reciprocal of -\frac{2}{39}.

$$x=-\frac{40}{13}\left(-\frac{39}{2}\right)$$

Multiply -\frac{40}{13} times -\frac{39}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-40\left(-39\right)}{13\times 2}$$

Do the multiplications in the fraction \frac{-40\left(-39\right)}{13\times 2}.

$$x=\frac{1560}{26}$$

Divide 1560 by 26 to get 60.

$$x=60$$