SOLUTION: If a and b are not equal, but ax=bx is a true statement, then find the numerical value of 2x (a+b).

Question 93837: If a and b are not equal, but ax=bx is a true statement, then find the numerical value of 2x (a+b).

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Subtract from both sides

Factor out x

Divide both sides by

Divide both sides by

Note: If we let x=0, we get which becomes and it will be true for any value of a and b

So that means if we evaluate with x=0, we get

Plug in x=0

Multiply

Distribute

Multiply

Add

So
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x must be zero so 2x(a+b) = 0
============
If you need an equation you could say:
ax=bx
x(a-b)=0
Either x = 0 or a-b=0
If a-b=0, a=b.
But we are told a does not equal b.
Therefore x must be zero.
Then 2x(a+b) = 2*0*(a+b) = 0
------------------
Cheers,
Stan H.
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