University Level Math Tutoring

I'm seeking a qualified tutor with expertise in both Algebra and Calculus, specifically in the areas of Inequalities, Gaussian Elimination, Alpha-Beta, proof by mathematical induction and permuations and combinations. This is for university level math, so a deep understanding of these topics is essential.

I want the tutor to solve the following questions (will provide screenshot with questions in proper format later):
1. Solve the following inequality and write your answer in set or interval notations:
|?^2 − 1| > |? − 3| − 2

3.3. Consider the following system of linear equations
{
? − 3? + 2? + 3? = 1
2? − 4? + 3? + ?
2? = −1
−3? + ? + ?? − ? = ?
}
where ? and ? are real numbers.
Using Gaussian elimination, determine all possible values of ? and ? such that the system has
(a) no solution;
(b) infinitely many solutions with one free variable;
(c) infinitely many solutions with two free variables.
Then solve the system in part (c).

4. If ?, ?, ? (where ?, ?, ? ≠ 0) are the roots of the equation ?^3 + ??^2 + ?? + ? = 0, where ?, ?
and ?(≠ 0) are real numbers, find a cubic equation (in terms of ?, ? and ?) whose roots are
(? + 1)/?? ,
(? + 1)/??
and
(? + 1)/??

5.Prove by mathematical induction that
4^? > ?^4
for all positive integers ? ≥ 5.

7. (a) How many different arrangements can be obtained from the letters of the word
LANGUAGE so that the letter N always appears before all the A’s?
(b) How many different arrangements can be obtained from the letters of the word ESSENCE
so that the first two letters are distinct?
(c) How many different arrangements can be formed by taking 5 letters from the word
TEMPERATURE? Assume that the letters are taken without replacement