Question

write an equivalent expression by distributing the \-\ sign outside the parentheses: 0.5r - (-10s - 2)

Explanation:

Step1: Recall the distributive property of subtraction

When we have a minus sign in front of a parenthesis, it's equivalent to multiplying each term inside the parenthesis by -1. So for the expression \(0.5r - (-10s - 2)\), we can rewrite the subtraction of the parenthesis as multiplying each term inside the parenthesis by -1. That is, \(0.5r+(- 1)\times(-10s - 2)\)

Step2: Distribute the -1

Using the distributive property \(a(b + c)=ab+ac\), here \(a=- 1\), \(b=-10s\) and \(c = - 2\). So \((-1)\times(-10s)+(-1)\times(-2)=10s + 2\)

Step3: Combine with the first term

The first term is \(0.5r\), so combining with the result from step 2, we get \(0.5r+10s + 2\)

Answer:

\(0.5r + 10s+2\)