## Precalculus (6th Edition) Blitzer

$(-\infty,-2)$.
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). --- $3[3(x+5)+8x+7]+5[3(x-6)-2(3x-5)] \lt 2(4x+3)$ .... 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 $(-\infty,-2)$.