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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
ax=bx

ax-bx=0 Subtract bx from both sides

x%28a-b%29=0 Factor out x

x=0%2F%28a-b%29 Divide both sides by a-b

x=0 Divide both sides by a-b

Note: If we let x=0, we get a%280%29=b%280%29 which becomes 0=0 and it will be true for any value of a and b



So that means if we evaluate 2x%28a%2Bb%29 with x=0, we get

2%280%29%28a%2Bb%29 Plug in x=0

0%28a%2Bb%29 Multiply

a%280%29%2Bb%280%29Distribute

0%2B0 Multiply

0 Add

So 2x%28a%2Bb%29=0

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x must be zero so 2x(a+b) = 0
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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
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Cheers,
Stan H.