Final answer:
The inequality -6z - 4(2z - 7) > 4z + 4 - 8z simplifies to -6z - 8z + 28 > -4z + 4. By combining like terms and isolating z, we find that z < 2.4 is the simplest form of the solution.
Step-by-step explanation:
To solve the inequality -6z - 4(2z - 7) > 4z + 4 - 8z, we first simplify both sides of the inequality:
-6z - 8z + 28 > 4z - 8z + 4
-14z + 28 > -4z + 4
Now, we isolate the variable z on one side. To do this, we add 4z to both sides:
-14z + 4z + 28 > 4
-10z + 28 > 4
Next, we subtract 28 from both sides to get:
-10z > 4 - 28
-10z > -24
To solve for z, we divide both sides by -10, remembering to flip the inequality sign because we are dividing by a negative number:
z < 24/10
z < 2.4
Therefore, the solution is z < 2.4, which means that z can be any number less than 2.4.