Question

use properties of operations to complete the equivale
10x - 5y = 5(__x - __y)
10x - 5y = 5(\square x - \square y)

Explanation:

Step1: Analyze the left - hand side

We have the expression \(10x - 5y\). We want to factor out a 5 from both terms. For the term \(10x\), when we factor out 5, we divide 10 by 5. Using the formula \(ab+ac=a(b + c)\) (the distributive property, here \(a = 5\), \(b=\frac{10x}{5}\), \(c=\frac{- 5y}{5}\)).
\(\frac{10x}{5}=2x\)

Step2: Analyze the second term

For the term \(-5y\), when we factor out 5, we divide \(-5y\) by 5.
\(\frac{-5y}{5}=-y\)
So \(10x - 5y=5(2x - 1y)\)

Answer:

The first blank is \(2\) and the second blank is \(1\) (or we can write it as \(10x - 5y = 5(2x-1y)\))