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

Answer:

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

Step-by-step 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,

$21.9x+32=21.9x+28$

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

$4\neq0$

Which is not possible means there is no solution.

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

Adding like terms,

$22x+32=21.9x+28$

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

$0.1x+4=0$

$0.1x=-4$

$x=\frac{-4}{0.1}$

$x=-40$

This equation has a solution.

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

Adding like terms,

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

$3.1x+2=0$

$3.1x=-2$

$x=\frac{-2}{3.1}$

$x=-0.64$

This equation has a solution.

Therefore, Option B is correct.