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How do you work 15 + 10x

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3 Answers

What's common about the coefficients?  Both 15 and 10 are divisible by 5.

So, 15 + 10x simplifies to 5(3+2x).

What do you notice about what's interior to the parentheses?  Both numbers are Prime.

Comments

I agree with this answer.

Kesiye

May I add that a common factor and coefficients in parentheses are all Fibonacci numbers? (Just for fun of it, they truly are)

Comment

Hi Rebecca,

It appears that people may be struggling with what you are actually asking. Joya did a nice job of leading you in the correct direction, but I will simply tell you the answer.  It appears that Richard saw your question from the opposite direction. Your original question appeared to be 5(3 + 2x) and you were asked to simplify it. That means to distribute the 5 into both of the terms inside the parentheses, which you did. You received 15 + 10x, correct? Joya was correct, you cannot combine constants (numbers) with coefficients (numbers attached to variables "letters") using addition and subtraction. It would be like adding some apples to oranges and claiming you have more apples now.  Therefore, your final answer in complete simplified form is 15 + 10x. I will let you know that some teachers prefer the answer say 10x + 15, but it is the same answer. Another example would be 6 - 9x would be the same as -9x +6, notice the sign stays with the term when I switch them thanks to the commutative property.  Simplifying regarding your question has nothing to do with getting the coefficients to be prime like Richard stated.

The goal of simplifying an equation is to get it to a place where you cannot make the answer any simpler.  Here's an example of an answer that is NOT simplified:

7x + 3x + 9 + 6

The reason this is not simplified is that there are multiple terms that can be combined.  The two terms with 'x' in them can be combined to form one term and the two constants (numbers without a variable attached) and be combined to form one number.  Remember that you CANNOT combine terms with variables with constants by addition or subtraction, only multiplication and division.  So 6(2x) can be simplified to 12x but 6 + 2x cannot be simplified any further.  

 

With all of that in mind, look at the terms 15 and 10x and ask yourself "can I combine these two terms?" If the answer is yes, then combine them.  If the answer is no, then you've arrived at your answer.

Comments

6 + 2x can indeed be simplified to 2(3+x), where all coefficients are Prime

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