Name the property which justifies the following conclusion:
given: 3q+9r
conclusion: 3(q+3r)
Distributive property.
3q+9r
The property that justifies the given conclusion is the distributive property of multiplication over addition.
To understand how to arrive at the conclusion and make use of the distributive property, let's break it down step by step:
Given: 3q + 9r
To get to the conclusion, 3(q + 3r), we need to apply the distributive property. According to the distributive property, when you have a number multiplied by a sum of terms, you can distribute the number to each term inside the parentheses.
In this case, the number being multiplied is 3, and the sum of terms inside the parentheses is q + 3r.
By applying the distributive property, we can distribute the 3 to each term inside the parentheses:
3q + 3(3r)
Now simplify the expression by multiplying 3 with each term inside the parentheses:
3q + 9r
Voila! We have arrived at the conclusion 3(q + 3r) by using the distributive property.