7 x _=2 x _

Question

how do i work out the problem 7 x _ = 2 x _

 

Answer 1

the answer is the empty set because the statement "7=2" is false

Answer 2

There is an infinite number of possibilities.

 

In the first blank, chose all multiples of 2.  In the second blank, chose any number that will give you the product of 7 times any number in the first blank respectively.  Note that multiplying any number by 2 will give you an even number, so any number multiplied by 7 must give you an even number .  For example.

 

 

7 × 4 = 2 × 14

 

7 × 6 = 2 × 21

 

7 × 8 = 2 × 28

 

7 × 10 = 2 × 35

 

 

The pattern in the second blank is that 7 is added from the previous possibility.

Answer 3

Without anything but 7x=2x the only solution is the trival solution, x=0. Mathematically rearranging... 7x-2x=0.      5x=0.   Therefore x=0. 

 

Hope that helps. 

 

*****Edit*****

 

i thought you were dealing with variables.  If you aren't dealing with a number that has to be the same, it is true that 7x2=2x7. If they must be the same, you are right it is zero.