How do you solve abs(x-3)-6=2|x3|6=2?

2 Answers
Mar 14, 2018

See a solution process below:

Explanation:

First, add color(red)(6)6 to each side of the equation to isolate the absolute value function while keeping the equation balanced:

abs(x - 3) - 6 + color(red)(6) = 2 + color(red)(6)|x3|6+6=2+6

abs(x - 3) - 0 = 8|x3|0=8

abs(x - 3) = 8|x3|=8

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

x - 3 = -8x3=8

x - 3 + color(red)(3) = -8 + color(red)(3)x3+3=8+3

x - 0 = -5x0=5

x = -5x=5

Solution 2:

x - 3 = 8x3=8

x - 3 + color(red)(3) = 8 + color(red)(3)x3+3=8+3

x - 0 = 11x0=11

x = 11x=11

The Solution Set Is:

#x = {-5, 11}

Mar 14, 2018

{x-3>0{x3>0
{-x+3>0{x+3>0

So it's either x-3x3 or -x+3x+3 and you put both of these separate

x-3-6=2x36=2 from where x=11x=11

and

-x+3-6=2x+36=2 from where x=-5x=5