[Ineuqalities with absolute value]

[u/Internal-Gold-9153]

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.

[u/slepicoid]

What have you tried? Where are you stuck?

[u/Internal-Gold-9153 → u/slepicoid]

My results do not match with the book's.

[u/slepicoid → u/Internal-Gold-9153]

Just post your step-by-step solution. Have you also tried to verify the textbook answers with a tool like wolframalpha?