Question

Which equation has no solution?

A.
4x − 9 = − 9

B.
3x + 2 = 17

C.
2x + 4 =2x + 6

D.
x + 3x = 8x − 4x

Answer 1

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`