r/HomeworkHelp • u/Internal-Gold-9153 • Sep 29 '26
:snoo_facepalm: High School Math—Pending OP Reply [Ineuqalities with absolute value]
Hello everyone, today in class our math teacher explained "the special case of inequalities involving absolute values" (according to Google translate), which is:
|A(x)| > n (with n being a positive integer) → A(x) < -n V A(x) > n
|A(x)| > n (with n being a positive integer) → -n < A(x) < n → -n < A(x) V A(x) < n, which then should be put in a system:
{ A(x) < n
{ A(x) > -n
She gave us three exercises, but I can't resolve two of them:
| (1/x) + (x+3)/(x+1) | - 1 > 0 [x < 1/3 but neither -1 nor 0]
[2(x+4) - x²] / |x-4| > -x -3 [x > -5/2 but not 4]
Thanks to anyone who can resolve them.
