Algebra

Absolute Value Inequalities

Absolute Value Inequalities - 2 Linear Terms

         

Solve for x:x: x+3+x3>16. \lvert x + 3 \rvert + \lvert x-3 \rvert > 16 .

How many integers xx satisfy the inequality 3x1+4x+145?3\lvert x-1 \rvert + 4\lvert x+1 \rvert \le 45?

If the solution to the inequality 7x+66x+77\lvert x+6 \rvert \le 6\lvert x+7 \rvert is αxβ,\alpha \le x \le \beta, what is 13(α+β)?13(\alpha+\beta)?

How many integers xx satisfy the inequality x1513?\big\lvert \lvert x-1 \rvert -5 \big\rvert \le 13?

What is the range of xx that satisfies the inequality x+1+x24x+4<x+82?\lvert x+1 \rvert + \sqrt{x^2-4x+4}<x+82?

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