Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
15x-45=15x+7515x−45=15x+7515, x, minus, 45, equals, 15, x, plus, 75

(Choice B)
B
45x-45=-15x+7545x−45=−15x+7545, x, minus, 45, equals, minus, 15, x, plus, 75

(Choice C)
C
-45x-45=-75x+75−45x−45=−75x+75minus, 45, x, minus, 45, equals, minus, 75, x, plus, 75

(Choice D)
D
15x-45=75x+7515x−45=75x+7515, x, minus, 45, equals, 75, x, plus, 75

A linear equation is solvable until we arrive at an absurd condition that is unintelligible. Or, if we end up with an equation with 0 as the coefficient of x and a non-zero constant number equal to 0 then we call that the equation is unsolvable.

For example 3x+5=3x+7 ⇒0x+(7-5)=0 ⇒ 2=0 which is absurd. Therefore the equation 3x+5=3x+7 is "unsolvable".

How to find out the unsolvable equation?

A) Has no solution because the equation is
15x-45=15x+75

⇒ -45=75 ⇒ 120=0 which is unintelligible.

B) This equation is solvable because,

45x-45=-15x+75

⇒60x=120

⇒x=2

C)This equation is also solvable because,

-45x-45=-75x+75

⇒(75-45)x=75+45

⇒30x=120

⇒x=4

D) This equation is also solvable because,

15x-45=75x+75

⇒ (75-15)x=-(75+45)=-120

⇒ 60x=-120

⇒ x=-2

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