HOW TO FIND THE VALUE OF Y FOR THE GIVEN VALUE OF X

Question

So I know the answer is 54, but my teacher didn't explain why, so I was hoping someone here could explain how she got that.

y=2x³ ; x=3 

 

So what I did was multiply 2x2x2 because exponents usually come first, then I got 8. After that I just multiplied that by 3, and got 24. I'm not sure what I am doing wrong. 

Answer 1

y=2x³ ; x=3

 

You are correct that exponents come first before multiplications.  One way to remember the order of operations is "PEMDAS", which stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.  

 

Actually, the order is parentheses, exponents or roots, multiplication or division, addition or subtraction.

 

After you get enough experience with solving these problems, you won't have to think about PEMDAS.  

 

Anyway, the important thing here is the the exponent "3" only applies to the "x".  Also, "x" is the variable here and it has a value of "3" (you know that because it says x=3 after the semicolon).  

 

So you can plug the value "3" into the first equation:

y = 2x³ ; x = 3

y = 2·3³

y = 2·27

y = 54

 

 

Note: If there were parentheses around the "2x", then the answer would be different.

y = (2x)³ ; x=3

y = [2·3]³

y = 6³

y = 216

 

Also note:  What you did (when you tried 2x2x2) would have been correct if the problem said

y = 2³·x  ; x=3

y = 2·2·2·x

y = 2·2·2·3

y = 8·3 

y = 24

 

 

 

Answer 2

Hi Nina,

First, plug in the value of x into the equation. Once you do that, the equation is y = 2*(3)^3, or you can write that as y= 2*(3*3*3). That simplifies to y = 2*(27), and the product of 2 and 27 is 54, the answer that your teacher gave you. When given the value of x, plug that value into the equation, and you can then solve for the value of other variable (y). Hope that helps. If you're interested in more help, I'd be happy to meet with you to solve other problems.

Answer 3

Hi Nina;

y=2x³

y=(2)(3³)

y=(2)(3)(3)(3)

y=(2)(27)

y=54

You multiplied 2 three times.  But x does not equal 3.

You must multiply 3 three times because x=3.