Answer:
i. = b
ii = d
iii = a
iv = c
Explanation:
When dividing an inequality with a negative number, remember to flip the inequality symbol:
- Less than (<) flips to greater than(>).
- Less than or equal to (≤) flips to greater than or equal to (≥).
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![\sf \implies 4x + 12 - 12 < 20 - 12\ \textsf{[ Subtract \boldsymbol{\sf 12} from both sides. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/77q1d5k3lsx3dns7rc8kahoc18pibxdmfz.png)
![\sf \implies 4x < 8\ \textsf{[ Divide both sides by \boldsymbol{\sf 4}. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/m0c6s22czukyipac1002dwr6gy321edmpb.png)
![\sf \implies (4x)/(4) < (8)/(4)\ \textsf{[ Simplify. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/dqyom5pb5at0e9lx4q771rf2438cfea4t4.png)

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![\sf \implies 55 - 35 < 35 - 35 + 10x\ \textsf{[ Subtract \boldsymbol{\sf 35} from both sides. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/kkaqcxhf9w4seq24pg0dbutqwjj950qxhf.png)
![\sf \implies 20 < 10x\ \textsf{[ Divide both sides by \boldsymbol{\sf 10}. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/n6jy1jcxfisc1zd83ccrpqmf38dy0omm8b.png)
![\sf \implies (20)/(10) < (10x)/(10)\ \textsf{[ Simplify. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/3p2u8iudvgruggp392bm6ivvkid6bexpov.png)

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![\sf \implies -(3)/(2)x + 12 - 12 > 15 - 12\ \textsf{[ Subtract \boldsymbol{\sf 12} from both sides. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/eakz1qvno28wom95rai0gt13z0pnu3peof.png)
![\sf \implies -(3)/(2)x > 3\ \textsf{[ Multiply both sides by \boldsymbol{\sf 2}. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/oclv47vt7xcfuj9696j1utd63rj6hogq8d.png)

![\sf \implies -3x > 6\ \textsf{[ Divide both sides by \boldsymbol{\sf -3}. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/oewkibn2s6x1mb5xtujtaks5sh5imvpkq8.png)
![\sf \implies (-3x)/(-3) > (6)/(-3)\ \textsf{[ Simplify. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/9s6sbx60g90bvj5j6jmdheap5d9ifinw8q.png)

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![\sf \implies (-8x)/(-8) < (16)/(-8)\ \textsf{[ Divide both sides by \boldsymbol{\sf -8}. ]}](https://img.qammunity.org/2023/formulas/mathematics/high-school/hrb59at0xwiy5juzj0ml6qt3ps4cldkedy.png)

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