Question

Which equation has no solution?

A). 24x + 32 − 2.1x = 20.9x + 30 + x + 2
B). 24x + 32 − 2.1x = 20.9x + 30 + x − 2
C). 24x + 32 − 2x = 20.9x + 30 + x − 2
D). 24x + 32 = 20.9x + 30

Answer 1

It's D because I don't see no solution

Answer 2

Option B -
`24x + 32 -2.1x = 20.9x + 30 + x - 2`

Explanation:

To find : Which equation has no solution?

Solution :

We find the solution of the equations one by one,

A)
`24x + 32 -2.1x = 20.9x + 30 + x + 2`

Adding like terms,

`21.9x+32=21.9x+32`

`21.9x+32-21.9x-32=0`

`0=0`

Which means for any value of x the equation is true.

B)
`24x + 32 -2.1x = 20.9x + 30 + x - 2`

Adding like terms,

`21.9x+32=21.9x+28`

`21.9x+32-21.9x-28=0`

`4\\eq0`

Which is not possible means there is no solution.

C)
`24x + 32 -2x = 20.9x + 30 + x - 2`

Adding like terms,

`22x+32=21.9x+28`

`22x+32-21.9x-28=0`

`0.1x+4=0`

`0.1x=-4`

`x=(-4)/(0.1)`

`x=-40`

This equation has a solution.

D)
`24x + 32= 20.9x + 30`

Adding like terms,

`24x + 32-20.9x-30=0`

`3.1x+2=0`

`3.1x=-2`

`x=(-2)/(3.1)`

`x=-0.64`

This equation has a solution.

Therefore, Option B is correct.