Solve for x: 3x − 7 = 2x + 5.

## The reasoning To solve for x, we need to get all terms with x on one side and all numbers on the other. Starting with: **3x − 7 = 2x + 5** **Step 1:** Subtract 2x from both sides 3x − 2x − 7 = 2x − 2x + 5 x − 7 = 5 **Step 2:** Add 7 to both sides x − 7 + 7 = 5 + 7 x = 12 This is the **principle of maintaining equality** — whatever you do to one side, you must do to the other. ## Why the wrong options tempt you **A) 10** — You might get this if you mistakenly did 5 + 7 = 12, then subtracted 2 somewhere. Calculation error. **C) −12** — This happens if you moved the 7 incorrectly and forgot to change its sign, ending up with x = −12. **D) 2** — You probably subtracted 3x from both sides instead of 2x, or mixed up the operations entirely. ## Quick takeaway **"Collect like terms: x's on one side, numbers on the other, and always perform the SAME operation on BOTH sides."** Master this and linear equations become your friend!