Question

choose an action to perform.
ways to rewrite expressions
combine like terms
distribute
perform multiplication
rewrite division as multiplication
rewrite fractions
rewrite signs
equation transformations
add to both sides
subtract from both sides
multiply both sides
divide both sides
-4 + \frac{z}{5} = -4

Explanation:

Step1: Analyze the equation

The equation is \(-4 + \frac{z}{5} = -4\). We want to solve for \(z\). First, we can use the "Add to both sides" transformation to eliminate the \(-4\) on the left.

Step2: Add 4 to both sides

Add 4 to both sides of the equation: \(-4 + 4 + \frac{z}{5} = -4 + 4\). Simplifying, we get \(\frac{z}{5} = 0\).

Step3: Multiply both sides by 5

Now, use the "Multiply both sides" transformation. Multiply both sides by 5: \(5\times\frac{z}{5} = 0\times5\), which gives \(z = 0\). But if we just consider the first step to start solving, the action from "Equation Transformations" is "Add to both sides" (adding 4 to both sides) and from "Ways to Rewrite Expressions", there's no direct rewrite needed here initially, but the key equation transformation step is adding 4 to both sides.

Answer:

From Equation Transformations, the action is "Add to both sides" (specifically add 4 to both sides to start solving \(-4 + \frac{z}{5} = -4\)). If choosing from the given options in Equation Transformations, the correct action is "Add to both sides" (to eliminate the -4 on the left).