Final answer:
The solution to the inequality 7|3x+2|+8>36 involves isolating the absolute value, setting up two separate inequalities, solving both, and expressing the answer in interval notation: (-\infty, -2) \cup (2/3, \infty).
Step-by-step explanation:
To solve the inequality 7|3x+2|+8>36, first we subtract 8 from both sides to isolate the absolute value:
7|3x+2| > 28
Now, we divide both sides by 7 to get the absolute value by itself:
|3x+2| > 4
This sets up two separate inequalities because if the expression inside the absolute value is positive, it's greater than 4, and if it's negative, its opposite must be greater than 4. Thus:
3x+2 > 4 or 3x+2 < -4
For 3x+2 > 4:
3x > 2
x > 2/3
For 3x+2 < -4:
3x < -6
x < -2
The solution in interval notation is (-\infty, -2) \cup (2/3, \infty).