|5x+3|+|2x+1|=|7x+4|

5х+3=0 х = -3/5

2х+1=0 х = -1/2

7x+4=0 x = -4/7

-,-,- +;-;- +;-;+ +;+;+

------'--------'----------'------->

-3/5 -4/7 -1/2

Раскроем знак модуля на каждом из интервалов:

1) $\left \{ {{x(-\infty;-3/5)} \atop {-5x-3-2x-1=-7x-4}} \right.$

-7x-4=-7x-4

0=0

2) $\left \{ {{x[-3/5;-4/7]} \atop {5x+3-2x-1=-7x-4}} \right.$

10x = -6

x = -0.6

3) $\left \{ {{x(-4/7;-1/2]} \atop {5x+3-2x-1=7x+4}} \right.$

-4x=2

x = -0.5

4) $\left \{ {{x(-1/2;+\infty)} \atop {5x+3+2x+1=7x+4}} \right.$

7x+4=7x+4

0=0

Ответ: х = -0,6. х = -0,5