Question

Which linear equation has no solution?

Answer 1

5x+12=5x-7 is the answer
because 0=-19 has no solution.

Answer 2

The linear equation that has no solution is: B) 5x + 12 = 5x - 7.

The linear equation that has no solution is the one that leads to a contradiction, meaning the left-hand side is not equal to the right-hand side. Let's analyze each equation:

1.
`\( (2)/(3)(9x + 6) = 6x + 4 \)`:

- Distributing on the left side:
`\( (2)/(3) \cdot 9x + (2)/(3) \cdot 6 = 6x + 4 \)`

- Simplifying:
`\( 6x + 4 = 6x + 4 \)`

- This equation is true for all values of x, so it has infinitely many solutions.

2.
`\( 5x + 12 = 5x - 7 \)`:

- Subtracting 5x from both sides: 12 = -7

- This equation is not true, leading to a contradiction. Therefore, it has no solution.

3.
`\( 4x + 7 = 3x + 7 \)`:

- Subtracting 3x from both sides:
`\( x + 7 = 7 \)`

- Subtracting 7 from both sides:
`\( x = 0 \)`

- This equation has a unique solution,
`\(x = 0\)`.

4.
`\( -3(2x - 5) = 15 - 6x \)`:

- Distributing on the left side:
`\( -6x + 15 = 15 - 6x \)`

- This equation is true for all values of x, so it has infinitely many solutions.

Therefore, the linear equation that has no solution is
`\(5x + 12 = 5x - 7\)`.