Question 213989
I need to identify each equation as being an identity, contradiction, or conditional equation. I need to verify my solution. Here is my problem:


{{{5x + 2 - 2x + 3 = 7x + 2 - x + 5 }}}


{{{5x + 2 - 2x + 3 = 7x + 2 - x + 5 }}}  Rearranging to collect x terms and numbers will yield


{{{5x-2x+2+3=7x-x+2+7}}}


{{{3x+5=6x+9}}}


Subtract 3x from both sides of equation to get x terms on right side


{{{3x+5-3x=6x+9-3x}}}


{{{5=3x+9}}}


Subtract 9 from both sides to get a number on left side and isolate x term


{{{5-9=3x+9-9}}}


{{{-4=3x}}}


Divide 3 to both sides of equation


{{{-4/3=3x/3}}}


{{{x=-4/3}}}


Let's verify the solution by substituting x=-4/3 into simplified equation below


 given as {{{5x + 2 - 2x + 3 = 7x + 2 - x + 5 }}} or simplifying {{{3x+5=6x+9}}}


{{{3*(-4/3)+5=6*(-4/3)+9}}}}  


Now check to see if left side = right side.  If it is then it's an identity.


{{{-4+5=2*(-4)+9}}}


{{{1=-8+9}}}


{{{1=1}}} So this is an identity and we can say that the solution is {{{x=-4/3}}}


I hope the above steps were helpful. 


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And good luck in your studies!


Respectfully,
Dr J