# What is the solution? (x+5)/5=1-((x+5)/7)

Jun 6, 2018

The solution is $x = - \frac{25}{12}$

#### Explanation:

Given $\frac{x + 5}{5} = 1 - \left(\frac{x + 5}{7}\right)$

Multiply both sides by 35:

$7 \left(x + 5\right) = 35 - 5 \left(x + 5\right)$

Distribute the 7 and the -5:

$7 x + 35 = 35 - 5 x - 25$

Add $5 x - 35$ to both sides:

$12 x = - 25$

$x = - \frac{25}{12}$

Jun 6, 2018

$\rightarrow \frac{x + 5}{5} = 1 - \frac{x + 5}{7}$

$\rightarrow \frac{x + 5}{5} + \frac{x + 5}{7} = 1$

$\rightarrow \left(x + 5\right) \left[\frac{1}{5} + \frac{1}{7}\right] = 1$

$\rightarrow \left(x + 5\right) \left[\frac{12}{35}\right] = 1$

$\rightarrow x = \frac{35}{12} - 5 = - \frac{25}{12}$