Tuesday, May 22, 2007

New Math

Original problem:
4 - 8x = -20


Solution:
use the commutative property to reverse the 8x and the 4*
8x - 4 = -20
Add 4 to both sides
8x = -16
divide both sides by 8
x = -2

Reasoning:

It's easier that way, mom.

Clearly we need to work on the commutative property in regard to subtraction.













For those of you who haven't done Algebra in a really long time, the solution should actually look like this:

4 - 8x = -20
*Since the commutative property applies only to addition and multiplication, we can't use it here.

Add 8x to both sides, add 20 to both sides:
4 + 20 - 8x + 8x = -20 + 20 + 8x

add:
24 = 8x

Divide both sides by 8:
3=x

Use the symmetric property:

x=3


3 comments:

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Dr. Momentum said...

Reversing the order of two terms in a subtraction flips the sign of the result. I have no idea whether there is a property for that.

4 - 8x = -20

8x - 4 = 20

8x -4 +4 = 20 +4

8x = 24

8x/8 = 24/8

x = 3

'Course, I'd never try to teach it to somebody that way. Your way is better.

Or, you can subtract the 4 from both sides and keep the x on the left.

-8x = -24 (divide out by -8)

x = 3

Judy said...

What you did was basically 2 steps. I teach that as multiply by -1 and then you can legitimately use the commutative property of addition to reverse the terms. OTOH, you don't really need to reverse the terms to add 4 to both sides once you've multiplied by -1.

You eventually have to multiply or divide by a negative number to reach the value of x.