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what is the value of 3xy+2x when x=2 and y=3?

8th grade algebra

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4 Answers

We are asked to find the value of the expression:

  3xy + 2x  in the case where x = 2 and y = 3.

This is a case of what I might call "numeric substition for variables".  It's a very important skill because it usually comes up at least once in many types of algebra and all kinds of science and math after that.

So let's make sure you understand this really well, and then you'll be all set for continued success with all kinds of interesting and important things!

The other answers posted here are absolutely correct. But I think a little more detail may be helpful to the student who is only discovering algebra for the first time.

In any algebra problem, you should be able to inspect the expression and identify the variables.  Here we see that there are two variables, right?  In this expression, one is named "x".  The other is named "y". They are called variables because the value they represent varies depending on the other facts of the problem.  They represent numbers whose actual value typically needs to be discovered by working with the facts that we do know, including rules about how equations can be manipulated without making them untrue.

These names may seem a bit boring, but when you have to write them over and over, you will appreciate that at least they are short, only one character long.

So in any case, "3xy" means "3 times x times y" and the expression is telling us to add the result of multiplying three values together to the result of multiplying two times the first variable ,x. 

I hope you agree that since the problem tells us that x=2, that means that for this problem, x and 2 are the same thing.  Since the problem is asking us for a "value" (rather than to say find the simplest expression), we know we need to choose the number form, 2 so that we can work out a numeric answer. 

However some people find it easier to see the substition, and avoid making certain kinds of mistakes afterwards, by learning how to use parentheses in equations. It is helpful to know how parentheses work in math when trying to use a calculator quickly and correctly, so this is another essential skill for life.

We had the following expression:

3xy + 2x.   It never hurts to re-write the question with just the variables substituted. If you substitute each value for its variable with parentheses around it, assuming you know the rules for calculations with parentheses in them, if after that, you have no letter variables left, at that point it is just a calculation.

= 3(2)(3) + 2 (2)   By writing it this way, we can quickly scan what we wrote and verify that we did this correctly.  X = 2, and Y = 3, scanning across we look at each value and think to ourselves "3*x*y + 2*y.. yep".  (All of this to this point should take five seconds, tops, or more practice is needed)

The rules for parentheses say that you have to complete any operations inside the brackets first. In this case, there are no remaining operations inside the parentheses (no add or subtract signs, for example).

The other rule is complete all multiplications before additions.   So in this problem for our next line, we would write: (because 3 * 2 * 3  = 18 is the product of the first three numbers, or in the other words, the first term of the expression, and 4 is the product of the two numbers in the second term of the expression). 

= 18 + 4

= 22  



Substitute the variables for the given numbers into the equation

3xy+2x x=2 y=3 ---> 3(2)(3) + 2(2)

Use PEMDAS to solve. Multiply first

3(2)(3) + 2(2) ---> 18 +4

Then Add. Solve.

18 +4 ---> 22

Remember "Please Excuse My Dear Aunt Sally" when you do this problem. Plug the variables into the equation, and you are given the following:

3 x (2x3) + (2x2)

3 x 6 + 4

18 + 4 = 22

Just replace the variables with the values given:

3 * (2*3) + (2*2)

3 * 6 + 4

18 + 4 = 22