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

1 Answer
Dec 15, 2017

Answer:

#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)#