Video Transcript
Use the properties of real
numbers to rewrite six multiplied by 𝑥 plus three as an equivalent expression
that does not contain parentheses.
In this question, we’re given
an algebraic expression six multiplied by 𝑥 plus three. And we want to find an
equivalent expression to this algebraic expression. However, we want this to not
contain any parentheses. And we’re told that we should
do this by using the properties of real numbers.
The first thing we need to do
is determine which of the properties of real numbers we can use to simplify our
algebraic expression. And to do this, we’re going to
need to look at our algebraic expression. Since our algebraic expression
involves multiplying the sum of two things, we could try simplifying this by
using the distributive property of multiplication over addition. Remember, this means whenever
we’re adding two numbers together and then multiplying the result, we can
instead multiply each of our terms together and then add the result.
Multiplying six by the first
term inside of our parentheses, we get six multiplied by 𝑥. Then remember we need to add
six multiplied by the second term in our parentheses, which we know gives us six
multiplied by three. Now all we need to do is
simplify this expression. First, remember, we can
simplify six multiplied by 𝑥 to just be six 𝑥. Next, we can evaluate six
multiplied by three is equal to 18. And now we can see this is
equivalent to our original expression; however, it doesn’t contain any
parentheses. Therefore, this gives us our
final answer.
We were able to show by using
the distributive property of multiplication over addition that six multiplied by
𝑥 plus three is exactly the same as six 𝑥 plus 18.
