The following sentence contains a blank that must be filled with the most appropriate phrasal verb in standard English usage. Four alternatives are given. Choose the option that correctly completes the sentence. I hope you know that, once you have signed the contract, you will not be able to _______.

Introduction / Context:
This question tests knowledge of common English phrasal verbs used in everyday formal and informal communication. In particular, it focuses on the expression used when a person withdraws from an agreement or obligation after initially accepting it. Understanding such phrasal verbs is important for both spoken and written English because they carry meanings that are often not obvious from the individual words alone. The sentence about signing a contract is a realistic business context where precise language is necessary.

Given Data / Assumptions:

• The action described happens after a person has already signed a formal contract.
• Once signed, the person is not allowed to withdraw from the agreement.
• The blank must be filled with a phrasal verb beginning with the word back.
• The sentence should sound natural and grammatically correct in standard English.

Concept / Approach:
Phrasal verbs are formed by combining a verb with one or more particles such as prepositions or adverbs. The meaning of the whole expression is often idiomatic. The phrase back out is commonly used to mean withdraw from an agreement, promise, or arrangement. Other combinations with back in, back up, and back at have different meanings that do not fit the context of cancelling a contractual commitment. Therefore, we need to select the phrasal verb whose established meaning matches the idea of withdrawing from a contract.

Step-by-Step Solution:
Step 1: Read the complete sentence and identify the situation, which is signing a contract and then trying to avoid fulfilling it. Step 2: Recall the meaning of back out, which is to withdraw from a promise, arrangement, or agreement after agreeing to it. Step 3: Check the meaning of back in, which usually relates to reversing a vehicle or returning to a place, and see that it does not fit the contractual context. Step 4: Consider back up, which normally means support, move backward, or create a copy of data, and note that it does not express withdrawal from a contract. Step 5: Evaluate back at, which is not a standard phrasal verb expressing cancellation of an agreement. Step 6: Conclude that only back out accurately completes the sentence with the intended meaning.

Verification / Alternative check:
A good way to verify is to replace the blank with each option and read the full sentence. I hope you know that, once you have signed the contract, you will not be able to back out sounds natural and clearly means you will not be able to withdraw. The other combinations sound strange or change the meaning completely. Additionally, dictionaries and exam preparation materials frequently use back out in examples involving cancellation of agreements, which supports this choice.

Why Other Options Are Wrong:
Back in usually refers to reversing a vehicle into a space or returning to a previous position, so it has no connection with cancelling a contract. Back up means to move backward, give support, or make a copy of data, none of which match the idea of withdrawing from a signed agreement. Back at is not a standard phrasal verb with a clear meaning here, so it does not fit the blank in a natural way.

Common Pitfalls:
Learners sometimes select phrasal verbs based only on individual word meanings. Seeing back, they may think of the physical direction behind them and ignore idiomatic usage. Another common mistake is to confuse back out with back up because both begin with the same base verb. To avoid this, always learn phrasal verbs as complete units with their meanings and example sentences rather than guessing from the separate words.

Final Answer:
The correct phrasal verb that completes the sentence is back out.