To solve an absolute inequality, we rewrite it as two separate inequalities: 5x + 6 < 8 and 5x + 6 > -8.
Let's start solving the inequality 5x + 6 < 8:
1. To isolate 5x, we subtract 6 from each side of the inequality: 5x < 8 - 6.
2. Now we have 5x < 2.
3. Next, to solve for x, we divide each side by 5: x < 2 / 5.
Therefore, the solution of this inequality is x < 0.4.
Next we move to the inequality 5x + 6 > -8:
1. Subtract 6 from each side of the inequality to isolate 5x: 5x > -8 - 6.
2. Now we have 5x > -14.
3. Divide each side by 5 to solve for x: x > -14 / 5.
Consequently, the solution of this inequality is x > -2.8.
Taking into account the solutions of both inequalities, an x value that satisfies the original inequality is a number that is greater than -2.8 and less than 0.4 at the same time. Therefore, the solution set of |5x + 6| < 8, expressed in interval notation, is (-2.8, 0.4).