E Which inequality has no solution? 6(x+2) > X-3 REME mellan ME 3+4x < 2(1+2x) f -2(x+6) O X-9<3(x-3)

 To determine which inequality has no solution, we must solve each inequality separately.

For the first inequality:

1. 6(x + 2) > x - 3

- Distribute the 6: 6x + 12 > x - 3 - Subtract x from both sides: 5x + 12 > -3 - Subtract 12 from both sides: 5x > -15 - Divide both sides by 5: x > -3

Since x can take on any value greater than -3, this inequality does have solutions.

For the second inequality:

2. 3 + 4x < 2(1 + 2x)

- Distribute the 2: 3 + 4x < 2 + 4x - Subtract 4x from both sides: 3 < 2

The statement 3 < 2 is never true, so this inequality has no solution.

For the third inequality:

3. x - 9 < 3(x - 3)

- Distribute the 3: x - 9 < 3x - 9 - Subtract x from both sides: -9 < 2x - 9 - Add 9 to both sides: 0 < 2x - Divide both sides by 2: 0 < x

Since x is greater than 0, this inequality does have solutions.

Therefore, the inequality that has no solution is the second one: 3 + 4x < 2(1 + 2x).