Question 157853
# 1


The equations 9x-3=15 and 5x + 4=14 are equivalent if they have the same solution. 



So let's solve 9x-3=15 



{{{9x-3=15}}} Start with the given equation.



{{{9x=15+3}}} Add {{{3}}} to both sides.



{{{9x=18}}} Combine like terms on the right side.



{{{x=(18)/(9)}}} Divide both sides by {{{9}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.




So the solution of {{{9x-3=15}}} is {{{x=2}}} 




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Now let's solve 





{{{5x+4=14}}} Start with the given equation.



{{{5x=14-4}}} Subtract {{{4}}} from both sides.



{{{5x=10}}} Combine like terms on the right side.



{{{x=(10)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.




So the solution to {{{5x+4=14}}} is {{{x=2}}} 



Since the two equations have the same solution, this means that they are both equivalent.


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# 2



{{{7y-6=7y +3}}} Start with the given equation



{{{7(0)-6=7(0)+3}}} Plug in {{{y=0}}}



{{{0-6=0+3}}} Multiply



{{{-6=3}}} Combine like terms. Since the equation is <b>NOT</b> true, this means that {{{y=0}}} is <b>NOT</b> a solution.