# How do you solve abs(-4-3n)/4=2?

Dec 15, 2017

$\textcolor{b l u e}{n = - 4 \mathmr{and} n = \frac{4}{3}}$

#### Explanation:

We are given an equation with an absolute value function

color(red)(|-4-3n|/4 =2 ... Equation.1

Multiply both sides of the equation by $4$

color(red)(|-4-3n|/4 =2

color(red)(4*|-4-3n|/4 =2*4

On simplification we get,

$\Rightarrow \cancel{4} \cdot | - 4 - 3 n \frac{|}{\cancel{4}} = 2 \cdot 4$

$\Rightarrow | - 4 - 3 n | = 8$ ... Equation.2**

We have the formula:

color(blue)(|f(n)| = a rArr f(n) = -a or f(n) = a

Using the above formula,

we can write ... Equation.2 as

$\Rightarrow \left(- 4 - 3 n\right) = 8 \mathmr{and} \left(- 4 - 3 n\right) = - 8$

Consider $\left(- 4 - 3 n\right) = 8$ first

On simplification we get

$\left(- 3 n\right) = 8 + 4$

$\left(- 3 n\right) = 12$

Divide both sides by (-1) to move the negative sign to the right

$\frac{- 3 n}{-} 1 = \frac{12}{-} 1$

$\Rightarrow 3 n = - 12$

Therefore

$n = \left(- \frac{12}{3}\right) = - 4$ **

color(blue)(n = -4 ... Result.1

Next, we will consider

$\left(- 4 - 3 n\right) = - 8$

On simplification we get

$\left(- 3 n\right) = - 8 + 4$

$\left(- 3 n\right) = - 4$

Divide both sides by $\left(- 1\right)$ to remove the negative sign from both sides.

We get,

$3 n = 4$

Therefore,

color(blue)(n = 4/3 ... Result.2

Hence, our final solutions are

$\textcolor{b l u e}{n = - 4 \mathmr{and} n = \frac{4}{3}}$