Find the sum of the roots of the equation: | 3x-1 | = | 4x + 8 |

Equations with modulus are solved as follows: if | x | = | a |, then x = a and x = -a.

It turns out two equations: 3x – 1 = 4x + 8 (1) and 3x – 1 = – (4x + 8) (2).

1) 3x – 1 = 4x + 8;

3x – 4x = 8 + 1;

-x = 9;

x = -9.

2) 3x – 1 = – (4x + 8);

3x – 1 = -4x – 8;

3x + 4x = 1 – 8;

7x = -7;

x = -7/7 = -1.

The roots of the equation are -9 and -1. Find the sum of the roots of the equation: -9 + (-1) = -10.

Answer: The sum of the roots of the equation is -10.