Sum of all the roots of the equation ||2x-3|- | vedclass

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(C) The given equation is $||2x-3|-4|=2$. This implies two cases: Case $1$: $|2x-3|-4 = 2 \implies |2x-3| = 6$. This further splits into: $2x-3 = 6 \i

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$6$

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(C) The given equation is $||2x-3|-4|=2$. This implies two cases: Case $1$: $|2x-3|-4 = 2 \implies |2x-3| = 6$. This further splits into: $2x-3 = 6 \implies 2x = 9 \implies x = 4.5$. $2x-3 = -6 \implies 2x = -3 \implies x = -1.5$. Case $2$: $|2x-3|-4 = -2 \implies |2x-3| = 2$. This further splits into: $2x-3 = 2 \implies 2x = 5 \implies x = 2.5$. $2x-3 = -2 \implies 2x = 1 \implies x = 0.5$. The roots are $4.5, -1.5, 2.5, 0.5$. The sum of the roots is $4.5 - 1.5 + 2.5 + 0.5 = 6$.

Sum of all the roots of the equation $||2x-3|-4|=2$ is

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