Which of the following equations have no solutions? Choose all answers that apply: Choose all answers that apply: (Choice A) A 14x-23=14x-2314x-23=14x-2314, x, minus, 23, equals, 14, x, minus, 23 (Choice B) B - 23x-14=14x-23-23x-14=14x-23minus, 23, x, minus, 14, equals, 14, x, minus, 23 (Choice C) C 14x+23=14x-2314x+23=14x-2314, x, plus, 23, equals, 14, x, minus, 23 (Choice D) D - 14x+23=14x-23-14x+23=14x-23

14 x + 23 = 14 x - 23 has no solution ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation has NO solutions if the variable in the equation

disappear and the left hand side (L. H. S) not equal the right hand

side (R. H. S)

- The equation has infinite solutions if the variable in the equation

disappear and the left hand side equal the right hand side

* Now lets check which equation has no solution

A) 14 x - 23 = 14 x - 23

- Add both sides by 23

∴ 14 x = 14 x

- Subtract 14 x from both sides

∴ 0 = 0

∵ L. H. S = R. H. S

∴ The equation has infinite solutions

B) - 23 x - 14 = 14 x - 23

- Add both sides by 23

∴ - 23 x + 9 = 14 x

- Add 23 x to both sides

∴ 9 = 37 x

- Divide both sides by 37

∴ x = 9/37

∴ The equation has one solution

C) 14 x + 23 = 14 x - 23

- Subtract 23 from both sides

∴ 14 x = 14 x - 46

- Subtract 14 x from both sides

∴ 0 = - 46

∵ L. H. S ≠ R. H. S

∴ The equation has NO solutions

D) - 14 x + 23 = 14 x - 23

- Subtract 23 from both sides

∴ - 14 x = 14 x - 46

- Subtract 14 x from both sides

∴ - 28 x = - 46

- Divide both sides by - 28

∴ x = 23/14

∴ The equation has one solution

* 14 x + 23 = 14 x - 23 has no solution