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4 votes
Which equation has no solution?

A.
4x − 9 = − 9

B.
3x + 2 = 17

C.
2x + 4 =2x + 6

D.
x + 3x = 8x − 4x

User Jeevatkm
by
7.7k points

1 Answer

2 votes

Hello there!

Let's solve these equations one by one.


\boxed{\tt{1}}


\longmapsto\sf{4x-9=9}

  • Add 9 to both sides:


\longmapsto\sf{4x=-9+9}


\longmapsto\sf{4x=0}

  • Divide both sides by 4:


\longmapsto\sf{4x=0}\\\longmapsto\sf{x=0}


\dag\quad\bf{Conclusion:}\quad\dag

  • This equation does have a solution. Let's try the second one.


\boxed{\tt{2}}


\tt{3x+2=17}

  • Subtract 2 from both sides.


\tt{3x=15}

  • Divide both sides by 3.


\tt{x=5}


\dag\quad\bf{Conclusion:}\quad\dag

  • The second equation has a solution as well. Now we need to try the third one:


\boxed{\tt{3}}


\tt{2x+4=2x+6}

  • Subtract 2x from both sides:


\tt{2x-2x+4=6}\\\tt{4=6}

Uh oh, we've obtained a false statement!

Well as a matter of fact, it was supposed to happen, because you cannot take a number, multiply it times 2, add 4 to that product, then expect it to be equal to that same number times 2, plus 6.


\stackrel\star{\dag\quad\bf{Conclusion:}\quad\dag}

  • So this is the equation that doesn't have a solution!

Therefore, Option C is correct.

I hope this helps, feel free to ask if you have any queries regarding my answer or explanation. I also hope that you'll have a lovely day ahead! :)


\wp\rm{Rosalia}\wp

User Ballbin
by
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