# How do you solve –(14n – 8) = – (9n – 8) – 5n?

Aug 3, 2017

See a solution process below:

#### Explanation:

First, remove terms from their parenthesis being careful to manage the signs correctly.

$- 14 n 8 = - 9 n + 8 - 5 n$

Now, group and combine like terms on the right side of the equation:

$- 14 n 8 = - 9 n - 5 n + 8$

$- 14 n 8 = \left(- 9 - 5\right) n + 8$

$- 14 n 8 = - 14 n + 8$

Because both sides of the equation are exactly the same $n$ can be any real number. Therefore the solution to this problem is $n$ is the set of all Real Numbers or $n = \left\{\mathbb{R}\right\}$

Aug 9, 2017

$n$ $=$ $\mathbb{R}$, where $\mathbb{R}$ is any real number.

#### Explanation:

$- \left(14 n - 8\right)$ $=$ $- \left(9 n - 8\right) - 5 n$

$\implies$ $- 14 n + 8$ $=$ $- 9 n + 8 - 5 n$

$\implies$ $- 14 n + 8$ $=$ $- 9 n - 5 n + 8$

$\implies$ $- 14 n + 8$ $=$ $- 14 n + 8$

$\implies$ Since the equation is same on the both sides, the value of $n$ can be any real number.

$n$ $=$ $\mathbb{R}$