Problem Solving with Inequalities
Algebra, and more...

 1 HARD Given $$a>b>c>d>0$$, which of the following is the greatest? $$\frac{a}{d}$$$$\frac{c}{b}$$$$\frac{c}{d}$$$$\frac{a}{b}$$$$\frac{d}{a}$$

 2 HARD Solve $$3x^2-3 > 2x^2+2x$$

 3 HARD Solve $$2x-4 < 3x+7 < x+1$$

 4 HARD Solve $$x^4 > x^3$$

 5 HARD Solve $$x^4+x < x^3+x^2$$

 6 HARD Solve for $$x$$ where $$4x < 16$$ and $$-3x < -6$$