Simplify 3𝑥 + (25 + 22𝑥).
Simplify adding three 𝑥 to 25 plus 22𝑥.
There’s something that we can immediately notice and that is that we’re dealing with addition. And when we’re dealing with addition and grouping, the associative property of addition will help us out here.
The associative property of addition tells us that we can add our addends in any order that we would like. It also tells us that we can regroup them if we want.
And what we wanna do here is we want to regroup our addends based on like terms. Three 𝑥 and 22𝑥 are like terms. They both are being multiplied by the variable 𝑥. This means we can add them together. 25 doesn’t have a like term, so we just bring it down.
Once we rearrange and regroup, we can actually start to simplify by adding three 𝑥 and 22𝑥. Three 𝑥 plus 22𝑥 equals 25𝑥, and our whole number can’t be simplified any further, so we just bring the 25 down again. The simplified form of the problem we started with is 25𝑥 plus 25.
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