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

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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

This is an identity

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

3x+7=5x+6-2x+1=3x+7

3x+7=5x+6-2x+1=3x+7

it is true for all values of x

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