Question

Which equation has no solution?

Responses

2x−6x=4(1−x)−4
2 x − 6 x = 4 ( 1 − x ) − 4

6x−2x=4(1−x)−4
6 x − 2 x = 4 ( 1 − x ) − 4

2x−6x=4(1−x)+4
2 x − 6 x = 4 ( 1 − x ) + 4

6x−2x=4(1−x)+4
6 x − 2 x = 4 ( 1 − x ) + 4

Answer 1

The equation 2x - 6x = 4(1 - x) + 4 simplifies to 0 = 4, which is never true.

Therefore, this equation has no solution.

Therefore, the correct answer is: option " 2x - 6x = 4(1 - x) + 4"

Step-by-step explanation:

To determine which equation has no solution, we need to simplify and solve each equation. Let's begin:

• 2x − 6x = 4(1 − x) − 4: This simplifies to -4x = 4 − 4x − 4, which further simplifies to -4x = − 4x.

This equation simplifies to an identity (0 = 0) and therefore has infinitely many solutions.

• 6x − 2x = 4(1 − x) − 4: This simplifies to 4x = 4 − 4x − 4, which further simplifies to 4x = − 4x.

Transposing terms gives 8x = 0, which implies x = 0. This equation has one solution.

• 2x − 6x = 4(1 − x) + 4: This simplifies to -4x = 4 − 4x + 4, which further simplifies to -4x = − 4x + 4.

Transposing terms gives 0 = 4, which is never true. Thus, this equation has no solution.

• 6x − 2x = 4(1 − x) + 4: This simplifies to 4x = 4 − 4x + 4, which further simplifies to 4x = − 4x + 4.

Transposing terms gives 8x = 4, which implies x = 0.5. This equation has one solution.

=> Hence, the equation 2x − 6x = 4(1 − x) + 4 is the one that has no solution.