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Solve for xxx:∣x−7∣<15. \lvert x - 7 \rvert < 15.∣x−7∣<15.
How many positive integers less than 100 satisfy ∣13−x∣>85? \lvert 13-x \rvert > 85 ?∣13−x∣>85?
If the solution set to the inequality 2∣x−1∣+3∣x+1∣<142\lvert{x-1}\rvert+3\lvert{x+1}\rvert < 142∣x−1∣+3∣x+1∣<14 is α<x<β,\alpha < x < \beta,α<x<β, what is the value of 10(β−α)?10(\beta-\alpha)?10(β−α)?
How many integers xxx satisfy ∣x∣+∣20−x∣≤20?\left|x\right| + \left|20-x\right| \le 20?∣x∣+∣20−x∣≤20?
What is the smallest integer xxx that satisfies ∣x−6∣<2x−23? |x-6| < 2x-23?∣x−6∣<2x−23?
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