How do you solve #abs(-x-9)=1#?

Question

Isaiah Anthony · Accepted Answer

See the entire solution process below:

Because this equation contains an absolute value function it is a special case. The absolute value function takes any negative or positive term and transforms it into it's positive form. Therefore, there are two solutions to this problem. To solve you must take the term within the absolute value and solve for both the negative and positive form of what it is equated to. Solution 1) #-x - 9 = -1# #-x - 9 + color(red)(9) = -1 + color(red)(9)# #-x - 0 = 8# #-x = 8# #color(red)(-1) xx -x = #color(red)(-1) xx 8# #x = -8# Solution 2) #-x - 9 = 1# #-x - 9 + color(red)(9) = 1 + color(red)(9)# #-x - 0 = 10# #-x = 10# #color(red)(-1) xx -x = #color(red)(-1) xx 10# #x = -10# The solution to this problem is: #x = -8# and #x = -10#

Jace Anderson · Answer

undefined To solve the equation $|\text{-}x-9|=1$, you would consider two cases:

1. $\text{-}x-9 = 1$, which simplifies to $x = -10$.
2. $\text{-}x-9 = \text{-}1$, which simplifies to $x = -8$.

Therefore, the solutions are $x = -10$ and $x = -8$.