Question 681194
Determine if the following is an identity or contradiction. 
4(x+3)-5=4x+17
<br>If in solving the equation the variables (x's) are eliminated and the statement is true then it's an identity, if it's false it's a contradiction. <r>

{{{4(x+3)-5=4x+17}}}
{{{4x+12-5=4x+17}}}
{{{4x+7=4x+17}}}
{{{-4x+4x+7=-4x+4x+17}}}
{{{7=17}}}
The x's were eliminated and the statement is false, so this is a contradiction.

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What if...instead...you had:
4(x+3)-5=4x+7
This would be an Identity....
{{{4x+12-5=4x+7}}}
{{{4x+7=4x+7}}} 
Right here you can see both side are the same and this is an identity, but if you tried to get the x's on the same side you get.  
{{{-4x+4x+7=-4x+4x+7}}}
{{{7=7}}}
The x's were eliminated and the statement is true, so this is an identity.

Hope that helped.  Happy Calculating!!!