College Algebra, 2013a

2.4 Inequalities with Absolute Value and Quadratic Functions 213
8
y
y = |x − 1|
7
6
y =5
5
4
3
y =2
2
−8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9
x
4. We need to exercise some special caution when solving |x +1|≥ x+4
2 .AswesawinExample
2.2.1 in Section 2.2, when variables are both inside and outside of the absolute value, it’s
usually best to refer to the definition of absolute value, Definition 2.4, to remove the absolute
values and proceed from there. To that end, we have |x +1| = −(x +1) if x