Sum of all the roots of the equation $||2x-3|-4| = 2$ is
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When solving equations with nested absolute values, like $| |ax+b| - c | = d$, work from the outside in. First solve $|Y| = d$ to get $Y=d$ or $Y=-d$, where $Y = |ax+b|-c$. Then solve each of these resulting equations for $x$.