Let's analyze the properties of equality used in the solution step-by-step.
We start with the equation:
[tex]\[ 5x = 50 \][/tex]
To isolate \( x \), we need to divide both sides of the equation by 5. This is because we want to have \( x \) by itself on one side of the equation. When we divide both sides of an equation by the same nonzero number, it ensures that the equality remains true.
Performing the division on both sides:
[tex]\[ \frac{5x}{5} = \frac{50}{5} \][/tex]
Simplifying both sides, we get:
[tex]\[ x = 10 \][/tex]
This process uses the Division Property of Equality, which states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal.
So, the property of equality represented here is the Division Property of Equality.
