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This absolute value inequality $$5\left| 2x-3\right| + 3 < 23$$ is satisfied when $$x \in \left( - \frac{1}{2}, \ \frac{7}{2} \right)$$. When I ask Sage to solve it, with this command
solve(5*abs(2*x-3)+3<23, x)

[[(-1/2) < x, x < (3/2)], [x == (3/2)], [(3/2) < x, x < (7/2)]]