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Linear Inequalities

When is 2x greater than x? Compare algebraic expressions with linear inequalities.

Absolute Value

         

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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