Question

solve the equation below. what’s the value of z? next, you can use the distributive property to get rid of the parentheses on the left side of the equation. distribute the 3 on the left to rewrite the equation without parentheses. \\(\frac{3}{2}(4 + 3z) = 2 + 2z\\) \\(2 \cdot \frac{3}{2}(4 + 3z) = 2 \cdot (2 + 2z)\\) \\(3(4 + 3z) = 4 + 4z\\) \\(\square = 4 + 4z\\)

Explanation:

Step1: Apply Distributive Property

We have the equation \(3(4 + 3z)\) (after canceling the 2s). Using the distributive property \(a(b + c)=ab+ac\), where \(a = 3\), \(b = 4\), and \(c=3z\).
So, \(3\times4+3\times3z=12 + 9z\).

Step2: Now the equation is

After distributing, the left - hand side \(3(4 + 3z)\) becomes \(12+9z\), and the right - hand side is \(4 + 4z\). So the equation \(12 + 9z=4+4z\) is obtained. But for the current step (filling the box), we just need to expand \(3(4 + 3z)\) using the distributive property.

Answer:

\(12 + 9z\)