Which order? take cube root, or divide by 4 first? solving 4x^3 = 20

kensher

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Hello.

I'm a little confused about a math equation (it's related to my chemistry assignments).

If you have the following equation:

4x3 = 20

Do you first do cube root or do you first isolate the x (divide by 4)?

The reason I ask is that is seems that I first have to isolate the x, but I though that the order of operation told us to first to exponents before dividing.
obviously I'm a little confused.
 
Hello.

I'm a little confused about a math equation (it's related to my chemistry assignments).

If you have the following equation:

4x3 = 20

Do you first do cube root or do you first isolate the x (divide by 4)?

The reason I ask is that is seems that I first have to isolate the x, but I though that the order of operation told us to first to exponents before dividing.
obviously I'm a little confused.

Isolation - if possible - is generally the first step.

So yes - you should divide both sides by 4. Then cube-root....

You could take the cube-root first - but that would make the process unnecessarily complicated.
 
I agree with Subhotosh Khan, but with one exception. If the coefficient is a perfect cube (i.e. its cube root is an integer), and the right-side of the equals does not cleanly divide the coefficient, then you might want to take the cube root first. As an example:

8x3 = 27

Take the cube root of both sides:

2x = 3
x = 1.5

Whereas, if you'd divided first, you'd end up with:

8x3 = 27
x3 = (27/8)
x = cbrt(27/8) = 1.5

In the end, the answer's the same because the cube root of 27/8 is, of course, 1.5, but it's much more difficult to intuit that out without a calculator. Whereas, the first method can easily be done without a calculator.
 
Hello.

I'm a little confused about a math equation (it's related to my chemistry assignments).

If you have the following equation:

4x3 = 20

Do you first do cube root or do you first isolate the x (divide by 4)?

The reason I ask is that is seems that I first have to isolate the x, but I though that the order of operation told us to first to exponents before dividing.
obviously I'm a little confused.

The order of operations convention is used when you are evaluating an expression. In other words, if you needed to evaluate (ie find the value of) \(\displaystyle 4*2^3\), you would do the cube first and get \(\displaystyle 4*8 = 32\).
When you are solving an equation like the one you have, you are basically working backwards to isolate x, hence the need to "get rid of" or divide by the 4 first.
 
I agree with Subhotosh Khan, but with one exception. If the coefficient is a perfect cube (i.e. its cube root is an integer), and the right-side of the equals does not cleanly divide the coefficient, then you might want to take the cube root first. As an example:

8x3 = 27

Take the cube root of both sides:

2x = 3
x = 1.5

Whereas, if you'd divided first, you'd end up with:

8x3 = 27
x3 = (27/8)
x = cbrt(27/8) = 1.5

In the end, the answer's the same because the cube root of 27/8 is, of course, 1.5, but it's much more difficult to intuit that out without a calculator. Whereas, the first method can easily be done without a calculator.

Absolutely correct analysis - that is why in my statement I had put the "weasel" word "generally".

Watched too many Judge Judy shows....
 
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