Algebra

Absolute Value Linear Inequalities

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

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

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

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

What is the smallest integer $x$ that satisfies $|x-6| < 2x-23?$

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