Question

What is |18x + 9| + 1 > 64 put into an interval notation and on a graph?

Answer 1

$\bf |18x+9| + 1 > 64\implies \pm(18x+9)+1>64 \\\\[-0.35em] ~\dotfill\\\\ +(18x+9)+1>64\implies 18x+10>64\implies 18x > 54 \\\\\\ x >\cfrac{54}{18}\implies \boxed{x > 3} \\\\[-0.35em] ~\dotfill\\\\ -(18x+9)+1>64\implies -18x-9+1>64\implies -18x-8>64 \\\\\\ -8>64+18x\implies -72 > 18x\implies \cfrac{-72}{18}=x\implies \boxed{-4>x}$

Check the picture below.