Final answer:
To solve the equation 4 = 9 + |11z + 3|, subtract 9 from both sides, remove the absolute value, and solve for z in each equation: 11z + 3 = -5 and -11z - 3 = -5. The solution set for the equation is z = -8/11 and z = 2/11.
Step-by-step explanation:
To solve the equation 4 = 9 + |11z + 3|, we need to isolate the variable z. Here's how:
- Subtract 9 from both sides: -5 = |11z + 3|
- Remove the absolute value: -5 = 11z + 3 or -5 = -11z - 3
- Solve for z in each equation:
- 11z + 3 = -5: Subtract 3 from both sides, then divide by 11. You will get z = -8/11.
- -11z - 3 = -5: Add 3 to both sides, then divide by -11. You will get z = 2/11.
Therefore, the solution set for the equation 4 = 9 + |11z + 3| is z = -8/11 and z = 2/11.