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solve 3x+7=5x+2(3-x)+1

why would both x=x and 7=7 both be correct answers to this equation?

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Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi PJ;
 
3x+7=5x+2(3-x)+1
Let's distribute 2(3-x)...
3x+7=5x+6-2x+1
Let's combine like terms...
3x+7=3x+7
 
Let's subtract 7 from both sides...
-7+3x+7=3x+7-7
3x=3x
Let's divide both sides by 3...
3x/3=3x/3
x=x
 
3x+7=3x+7
Let's subtract 3x from both sides...
-3x+3x+7=3x+7-3x
7=7
Michael F. | Mathematics TutorMathematics Tutor
4.6 4.6 (5 lesson ratings) (5)
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This is an identity
3x+7=5x+2(3-x)+1
3x+7=5x+6-2x+1=3x+7
it is true for all values of x