Question

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

Answer 1

`color(blue)(n=-4 or n=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,

`rArr cancel4*|-4-3n|/cancel 4 =2*4`

`rArr |-4-3n| = 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

`rArr (-4-3n) = 8 or (-4-3n) = -8`

Consider `(-4-3n) = 8` first

On simplification we get

`(-3n) = 8 + 4`

`(-3n) = 12`

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

`(-3n)/-1 = 12/-1`

`rArr 3n = -12`

Therefore

`n = (-12/3) = -4` **

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

Next, we will consider

`(-4-3n) = -8`

On simplification we get

`(-3n) = -8 + 4`

`(-3n) = -4`

Divide both sides by `(-1)` to remove the negative sign from both sides.

We get,

`3n = 4`

Therefore,

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

Hence, our final solutions are

`color(blue)(n=-4 or n=4/3)`