The best way to correct the punctuation in the sentence is:
"Michelle Obama gained public support during her first months as first lady. In fact, she became a role model."
Step-by-step explanation:
1. The first option, "Michelle Obama gained public support during her first months as first lady in fact she became a role model," is incorrect. It lacks punctuation between the clauses "first lady" and "in fact."
2. The second option, "Michelle Obama gained public support during her first months as first lady; in fact; she became a role model," is also incorrect. The use of semicolons in this context is unnecessary and disrupts the flow of the sentence.
3. The third option, "Michelle Obama gained public support during her first months as first lady, in fact; she became a role model," is incorrect. It places a comma before "in fact," which creates a comma splice error.
4. The fourth option, "Michelle Obama gained public support during her first months as first lady; in fact, she became a role model," is the correct choice. It uses a semicolon to separate the clauses "first lady" and "in fact," which indicates a stronger connection between the two ideas. Additionally, it correctly uses a comma after "in fact" to separate it from the following clause.
By using a semicolon and a comma appropriately, the corrected sentence reads smoothly and maintains the intended meaning.