Question

solve the equation. what is the value of z? keep going. we’re trying to get z alone on one side and a constant alone on the other. we can make a balanced move so that the z terms are only on one side. we have -5z + 2 on the left. what move can we make to get rid of -5z on the left, so that all the z terms are on the right, while maintaining balance? 12 - 5(z + 2) = 3z - 10 12 - 5z - 10 = 3z - 10 -5z + 2 = 3z - 10 add 5z to both sides subtract 5z from both sides multiply both sides by 5z divide both sides by 5z

Explanation:

Step1: Analyze the goal

We want to eliminate \(-5z\) from the left side so that all \(z\)-terms are on the right. The left side has \(-5z\), and the right side has \(3z\). To get all \(z\)-terms on the right, we can add \(5z\) to both sides (since adding \(5z\) to \(-5z\) will cancel it on the left, and adding \(5z\) to the right will combine with \(3z\)).

Step2: Evaluate each option

• Add \(5z\) to both sides: Left side: \(-5z + 2+5z=2\), Right side: \(3z - 10+5z = 8z-10\). This moves all \(z\)-terms to the right.
• Subtract \(5z\) from both sides: Left side: \(-5z + 2-5z=-10z + 2\), Right side: \(3z - 10-5z=-2z - 10\). Now \(z\)-terms are on both sides, not desired.
• Multiply both sides by \(5z\): This complicates the equation and doesn't eliminate \(-5z\) from the left.
• Divide both sides by \(5z\): This also complicates and doesn't eliminate \(-5z\) (and may be undefined if \(z = 0\)).

Answer:

Add 5z to both sides