Question

solve the equation below. what’s the value of z? the equation. what move can you make to get rid of the 4z on the right side of the equation, 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\\) add 4z to both sides subtract 4z from both sides divide both sides by 4z multiply both sides by 4z

Explanation:

Step1: Recall Equation Balance

To eliminate \(4z\) from the right side (\(4 + 4z\)) and keep the equation balanced, we use the inverse operation of addition (since \(4z\) is added to 4). Subtracting \(4z\) from both sides will cancel \(4z\) on the right.

Step2: Analyze Options

• "Add \(4z\) to both sides" would add more \(z\)-terms, not eliminate.
• "Subtract \(4z\) from both sides" removes \(4z\) from the right (\(4 + 4z - 4z = 4\)) and adjusts the left side, maintaining balance.
• "Divide both sides by \(4z\)" is incorrect (division by \(4z\) is not needed here, and \(z\) could be 0, causing division by zero).
• "Multiply both sides by \(4z\)" introduces extra terms, not elimination.

Answer:

Subtract 4z from both sides