How do you solve the equation #abs(x+a)=b#?

1 Answer
Aug 24, 2017

Answer:

See a solution process below:

Explanation:

Assuming solving the equation for #x#:

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 + a = -b#

#x + a - color(red)(a) = -b - color(red)(a)#

#x + 0 = -b - a#

#x = -b - a#

Solution 2:

#x + a = b#

#x + a - color(red)(a) = b - color(red)(a)#

#x + 0 = b - a#

#x = b - a#

The Solutions Are:

#x = -b - a# and #x = b - a#

Or

#x = +-b - a#