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

1 Answer
Dec 15, 2017

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)