Question

Write each compound inequality as an absolute value inequality 1.3

Answer 1

Consider an absolute value inequality.

For example, 3≤|x-7|

this means that x-7 can be

i) 3,    3.4,    5,    7.5       etc
                                 
or   ii) -3,    -3.2,     -4.7    etc since these values in abs value all are ≥3
 

thus  the set of all values in i) is represented by x-7≥3, which means x≥10

and the set of all values in ii) is  x-7≤-3, which means x≤4.



Thus, the compound inequality is : x≥10  OR x≤4

an absolute inequality corresponding to this compound inequality is 3≤|x-7|