Linear Inequalities

Absolute Value Linear Inequalities


Solve for xx:x7<15. \lvert x - 7 \rvert < 15.

How many positive integers less than 100 satisfy 13x>85? \lvert 13-x \rvert > 85 ?

If the solution set to the inequality 2x1+3x+1<142\lvert{x-1}\rvert+3\lvert{x+1}\rvert < 14 is α<x<β,\alpha < x < \beta, what is the value of 10(βα)?10(\beta-\alpha)?

How many integers xx satisfy x+20x20?\left|x\right| + \left|20-x\right| \le 20?

What is the smallest integer xx that satisfies x6<2x23? |x-6| < 2x-23?


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