Question

Solve for \( z \) if \( 4z - 7 = 3z + 5 \).

Answer 1

Step 1: Move all the \( z \)-terms to one side and constants to the other.

Subtract \( 3z \) from both sides: \[ 4z - 7 - 3z = 3z + 5 - 3z \] Simplifies to: \[ z - 7 = 5 \]

Step 2: Add 7 to both sides to isolate \( z \).

\[ z - 7 + 7 = 5 + 7 \] Simplifies to: \[ z = 12 \]

Final Answer: \(\boxed{z = 12}\)

Short Explanation (Why this works)

To solve linear equations, we use the balance method: whatever you do to one side, do to the other. Here, we eliminated \( z \) from one side and then isolated it, leading to \( z = 12 \).