To simplify the expression \(3(z-4) + 2(x+1) + 4(z+2)\), we can distribute the terms and combine like terms.
-
Distribute \(3\) in the first term: \[ 3(z-4) = 3z - 12 \]
-
Distribute \(2\) in the second term: \[ 2(x+1) = 2x + 2 \]
-
Distribute \(4\) in the third term: \[ 4(z+2) = 4z + 8 \]
Now we can combine all the terms: \[ 3z - 12 + 2x + 2 + 4z + 8 \]
Now, group together the like terms:
-
Combine the terms involving \(z\): \[ 3z + 4z = 7z \]
-
Combine the constant terms: \[ -12 + 2 + 8 = -2 \]
Putting everything together gives us: \[ 7z + 2x - 2 \]
So, the simplified form of the expression \(3(z-4) + 2(x+1) + 4(z+2)\) is: \[ 7z + 2x - 2 \]