Question

For Items 5–7, fill in the blank to form an equation that has no solution.

___ + 12 − 3d = 5d + 6
___ (m − 2) = −2(–2m + 6)
____ + 2y − 8 = 3(y – 11)

Answer 1

For the equations to have no solution:

1. 0 + 12 - 3d = 5d + 6

2. 0 * (m - 2) = -2(-2m + 6)

3. 0 + 2y - 8 = 3(y - 11)

Step-by-step explanation:

To create equations with no solution, we aim to generate contradictions or inconsistencies in the equations. In the first equation, 0 + 12 - 3d = 5d + 6 simplifies to 12 - 3d = 5d + 6. Further simplification leads to 12 = 8d + 6, and subsequently, 6 = 8d, implying d = 3/4. However, substituting this value back into the original equation yields different results on both sides, leading to a contradiction.

In the second equation, 0 * (m - 2) = -2(-2m + 6). Multiplying by 0 simplifies the left side to 0, while the right side becomes 0 ≠ 4m - 12, resulting in an inconsistency.

Likewise, the third equation, 0 + 2y - 8 = 3(y - 11), simplifies to -8 = 3y - 33. Further simplification leads to 25 = 3y, implying y = 25/3. However, substituting this value back into the original equation causes an inconsistency. Therefore, all three equations have no solution as they lead to contradictions or inconsistencies and cannot be simultaneously satisfied.