Question

-2 + \frac{z}{5} = -2
choose an action to perform.
ways to rewrite expressions
combine like terms\tdistribute
perform multiplication\trewrite division as multiplication
simplify fractions\trewrite signs
equation transformations
add to both sides
subtract from both sides
multiply both sides
divide both sides

Explanation:

Step1: Analyze the equation

The equation is \(-2 + \frac{z}{5} = -2\). To solve for \(z\), we first want to isolate the term with \(z\). The first step is to get rid of the \(-2\) on the left side. We can do this by adding \(2\) to both sides (or applying the "Add to both sides" operation from the "Equation Transformations" table). Let's check: if we add \(2\) to both sides, we have \(-2 + 2 + \frac{z}{5} = -2 + 2\), which simplifies to \(\frac{z}{5}=0\). Then we can multiply both sides by \(5\) to solve for \(z\), but the first action here is to add \(2\) to both sides, which is the "Add to both sides" operation.

Step2: Confirm the action

Looking at the "Equation Transformations" table, the operation "Add to both sides" is applicable here. We add \(2\) to both sides to eliminate the \(-2\) on the left.

Answer:

From the "Equation Transformations" table, the action is "Add to both sides" (specifically, add \(2\) to both sides of the equation \(-2 + \frac{z}{5} = -2\)).