Posted by Julianna on .
Right now we are learning about absolute value inequalities. I have to solve and graph this inequality:
Pretend my paranpheses are absolute value signs
(x4) + 5 is greater than or equal to 10.
I assume I would take 5 away from each side first. But what would be the correct way to display this on a line, and what would be its set builder notation and interval notation?
Thank you so much! :)

Here's what I got... 
Julianna,
I took away 5 from each side and added 4 to each side. That got me
(x) is greater than or equal to 14.
Would this make the set builder notation be:
{x such as x is greater than or equal to 4}
And the interval notation be:
(negative infinity, 14] U [14, infinity)?
Thanks! :) 
Algebra 
drwls,
You have to consider two cases. I will leave out the = sign for convenience.
(1) If x  4 > 0, then
x  4 + 5 > 10
x > 9 (which satisfies the x>4 assumption)
(2) If x  4 < 0, then
If 4  x + 5 > 10, then
x > 1
x < 1
(which satisfies the x<4 assumption)