SOLUTION: Explain why 2 + 3(x – 2) = 5x – 10 is not true as a rule.

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Question 1100329: Explain why 2 + 3(x – 2) = 5x – 10 is not true as a rule.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2%2B3%28x-2%29
Distributive Property!

2%2B3x-6
3x%2B2-6
3x-4

The term '2' and the factor '3' ARE NOT GROUPED.

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Probably, you want to ask: 

    Explain why     2 + 3(x – 2) = 5x – 10  (*)  is not true identity.


It is because the left part is 

    2 + 3x - 6 = 3x - 4,


while the right side is 5x - 10.


The left side expression differs from that of the right side.
Therefore, (*) is not an identity.


We even can go further and write a hypothetical equation

3x - 4 = 5x - 10

which implies

2x = 6  and    then   x = 3.


So, the two original expressions are equal only at x = 3,  but they are not equal identically as functions.