Algebra

# Absolute Value Inequalities - 2 Linear Terms

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

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

If the solution to the inequality $7\lvert x+6 \rvert \le 6\lvert x+7 \rvert$ is $\alpha \le x \le \beta,$ what is $13(\alpha+\beta)?$

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

What is the range of $x$ that satisfies the inequality $\lvert x+1 \rvert + \sqrt{x^2-4x+4}

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