Problem Solving with Inequalities
Algebra, and more...

 1 EASY Solve $$3x-5 > 7$$

 2 EASY Solve $$7-2x < -3$$

 3 MEDIUM Given $$a > b > c > d$$, which of the following must be true? $$a-b>c-d$$$$ab>cd$$$$a+c>b+d$$$$\frac{a}{d}>\frac{c}{b}$$$$a+b>c+d$$

 4 MEDIUM If $$(x-3)^2 > (x-3)^3$$ and $$(x-3)^3\le0$$, which of the following is the most accurate range for x? $$x>3$$$$x\ge3$$$$x=3$$$$x\le3$$$$x<3$$

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

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

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

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

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

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