Answer:
[tex]-2<x+5<2[/tex]
[tex]x-8\leq5[/tex] Or [tex]x-8\geq5[/tex]
Step-by-step explanation:
Given inequalities:
[tex]|x+5|<2[/tex]
[tex]|x-8|\geq5[/tex]
To find their equivalent inequalities.
Solution:
For the inequality [tex]|x+5|<2[/tex] , we see that the absolute value expression [tex]x+5[/tex] has value less than 2 units on either direction of 0. Hence the value range will be an interval between -2 and 2.
Thus, the equivalent inequality for this will be:
[tex]-2<x+5<2[/tex]
For the inequality [tex]|x-8|\geq5[/tex], we see that the absolute value expression [tex]x-8[/tex]
has value greater than or equal to 5 units on either side of 0. Hence, the value can lie on two ranges that are [tex]\leq5[/tex] or [tex]\geq 5[/tex]
Thus, the equivalent inequality for this will be:
[tex]x-8\leq5[/tex] or [tex]x-8\geq5[/tex]
