Answer
$(-\infty,-2)$.
Work Step by Step
The idea is to isolate x on one side.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same).
Multiplying/dividing with a negative number inverts the order (the inequality symbol changes).
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$3[3(x+5)+8x+7]+5[3(x-6)-2(3x-5)] \lt 2(4x+3)$
.... distribute inner parentheses
$3 [3x+15+8x+7]+5[3x-18-6x+10] \lt 8x+6$
... simplify within the brackets
$3 [11x+22]+5[-3x-8] \lt 8x+6$
... distribute
$33x+66-15x-40 \lt 8x+6$
... simplify
$ 18x+26 \lt 8x+6 \qquad $ ... $/-8x-26$
$ 10x \lt -20 \qquad $ ... $/\div 10$
$ x \lt -2$
The solution set is $(-\infty,-2)$.
