Algebra
# Absolute Value Inequalities

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

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

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 $\lvert x+1 \rvert + \sqrt{x^2-4x+4}<x+82?$