Honors problem 10

Question

solve 3x+4=10 by using inverse multiplication first. Explain why it is better to use inverse addition first.

Answer 1

The goal here is to isolate the x terms and get the coefficient of x to be 1.  x has a coefficient of 3.  This means that you are multiplying x by 3.  In order to isolate that term, you need to subtract 4 on both sides of the equation.  Subtraction is the inverse of addition.  So when you do this, you get

 

3x = 6

 

Now you can use the inverse of multiplication, which is dividing both sides of the equation by 3 to get the coefficient of x to be 1.

Answer 2

3x + 4 = 10

 

Divide through by 3.

 

x + (4/3) = (10/3)

 

x = (10/3) - (4/3)

 

x = 6/3

 

x = 2

 

 

3x + 4 = 10

 

3x = 10 - 4

 

3x = 6

 

x = 6/3

 

x = 2

 

 

It is so much easier to lose a denominator or garble up your work and make a mistake when you  do inverse multiplication first.

 

Your problem goes from three terms to two terms almost immediately and is much easier to manage when you do inverse addition first.