Question

solve the equation below. what’s the value of z? subtract 4z from both sides of the equation to get rid of the 4z on the right, while keeping the equation balanced. \\(\frac{3}{2}(4 + 3z) = 2 + 2z\\) \\(2 \cdot \frac{3}{2}(4 + 3z) = 2 \cdot (2 + 2z)\\) \\(3(4 + 3z) = 4 + 4z\\) \\(12 + 9z = 4 + 4z\\) \\(\underline{\quad - 4z \quad \quad \quad \quad - 4z \quad}\\) \\(\square = \square\\)

Explanation:

Step1: Simplify Left Side

Subtract \(4z\) from \(12 + 9z\): \(12 + 9z - 4z = 12 + 5z\)

Step2: Simplify Right Side

Subtract \(4z\) from \(4 + 4z\): \(4 + 4z - 4z = 4\)

Answer:

\(12 + 5z = 4\) (Now, to find \(z\), we can continue: \(5z = 4 - 12 = -8\), so \(z = -\frac{8}{5}\). But for the current step, the left box is \(12 + 5z\) and the right box is \(4\))