Question

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

A) 5x+5=-4x-5 B) 4x+5=-4x+5
C) -4x+5=-4x-4
D) -4x+5=-4x-5

Answer 1

Equations C (-4x + 5 = -4x - 4) and D (-4x + 5 = -4x - 5) have no solutions because after canceling out the variable terms, the remaining constant terms are not equal.

Step-by-step explanation:

The equations that have no solutions are ones in which the same variable terms on both sides of the equation cancel each other out, but the remaining constant terms are not equal to each other.

• B) 4x + 5 = -4x + 5 cancels out to 8x = 0, which has a solution (x=0), so it is not a no-solution equation.
• C) -4x + 5 = -4x - 4 cancels out to 0x = 9, which is impossible, hence this equation has no solution.
• D) -4x + 5 = -4x - 5 also cancels out to 0x = 10, which is impossible, so this equation also has no solution.

Therefore, the equations that have no solutions are C and D.