To solve the equation |3(x+4)| + 8 = 23, you can follow these steps:
1. Subtract 8 from both sides of the equation:
|3(x+4)| = 23 - 8
|3(x+4)| = 15
2. Now, you have an absolute value equation. You need to consider both the positive and negative cases:
a) 3(x+4) = 15
b) -(3(x+4)) = 15
3. Solve each case separately:
a) 3(x+4) = 15
Divide both sides by 3:
x + 4 = 15/3
x + 4 = 5
Subtract 4 from both sides:
x = 5 - 4
x = 1
b) -(3(x+4)) = 15
Divide both sides by -3:
x + 4 = 15/(-3)
x + 4 = -5
Subtract 4 from both sides:
x = -5 - 4
x = -9
So, the solutions to the equation |3(x+4)| + 8 = 23 are x = 1 and x = -9.