This sentence is an example of a run-on or comma splice. It has two independent clauses separated only by a comma. One way to fix this is to change the comma to a semicolon; if this were to be done, the corrected sentence would read, "Thomas had always struggled with trigonometry; he thought that circles should remain circles and let triangles and squiggles be their own shapes."

This is an incorrect use of a semi-colon. If you use a semi-colon, you should not follow it with a conjunction. In this case, it sounds best to keep the conjunction “so” and switch the semi-colon to a comma: "Joe was feeling particularly happy on Tuesday, so he decided to treat himself to a cup of coffee and a slice of pie."

This is an incorrect use of a semi-colon. If you use a semi-colon, you should not follow it with a conjunction. In this case, it sounds best to keep the conjunction “so” and switch the semi-colon to a comma: "Joe was feeling particularly happy on Tuesday, so he decided to treat himself to a cup of coffee and a slice of pie."

This is an incorrect use of a semi-colon. If you use a semi-colon, you should not follow it with a conjunction. In this case, it sounds best to keep the conjunction “so” and switch the semi-colon to a comma: "Joe was feeling particularly happy on Tuesday, so he decided to treat himself to a cup of coffee and a slice of pie."

This sentence is an example of a run-on or comma splice. It has two independent clauses separated only by a comma. One way to fix this is to change the comma to a semicolon; if this were to be done, the corrected sentence would read, "Thomas had always struggled with trigonometry; he thought that circles should remain circles and let triangles and squiggles be their own shapes."

Here, "finally" is considered an introductory word, so it must be followed by a comma: "Finally, the teacher . . ."

Here, "finally" is considered an introductory word, so it must be followed by a comma: "Finally, the teacher . . ."

Here, "finally" is considered an introductory word, so it must be followed by a comma: "Finally, the teacher . . ."

This sentence is an example of a run-on or comma splice. It has two independent clauses separated only by a comma. One way to fix this is to change the comma to a semicolon; if this were to be done, the corrected sentence would read, "Thomas had always struggled with trigonometry; he thought that circles should remain circles and let triangles and squiggles be their own shapes."

This sentence has a comma splice, which means that it has two independent clauses separated only by a comma. A semicolon is appropriate here. The corrected sentence reads, "The city’s youth take great pride in the local music scene; there are popular concerts every weekend."