Answer
$(-\displaystyle \frac{3}{4},\infty)$ .
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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$5[3(2-3x)-2(5-x)]-6[5(x-2)-2(4x-3)] \lt 3x+19$
.... distribute inner parentheses
$5 [6-9x-10+2x]-6[5x-10-8x+6] \lt 3x+19$
... simplify within the brackets
$5 [-7x-4]-6[-3x-4] \lt 3x+19$
... distribute
$-35x-20+18x+24 \lt 3x+19$
... simplify
$-17x+4 \lt 3x+19 \qquad $ ... $/-3x-4$
$-20x \lt 15\qquad $ ... $/\div(-20)$ ... (negative: change direction)
$ x \gt \displaystyle \frac{15}{-20}$
$ x \gt -\displaystyle \frac{3}{4}$
The solution set is $(-\displaystyle \frac{3}{4},\infty)$ .
