How do you solve #abs(-x+9)=4#?

1 Answer
Mar 13, 2018

Answer:

See a solution process below:

Explanation:

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 + 9 = -4#

#-x + color(red)(x) + 9 + color(red)(4) = -4 + color(red)(4) + color(red)(x)#

#0 + 13 = 0 + x#

#13 = x#

#x = 13#

Solution 2:

#-x + 9 = 4#

#-x + color(red)(x) + 9 - color(red)(4) = 4 - color(red)(4) + color(red)(x)#

#0 + 5 = 0 + x#

#5 = x#

#x = 5#

The Solution Set Is: #x = {5, 13}#