Solve: 7y - 4 = 3y + 12.

**The reasoning** This is a **linear equation** — we need to get all the *y* terms on one side and all the numbers on the other. Start: 7y - 4 = 3y + 12 **Step 1:** Subtract 3y from both sides (to collect y's together) 7y - 3y - 4 = 12 4y - 4 = 12 **Step 2:** Add 4 to both sides (to isolate the y term) 4y = 12 + 4 4y = 16 **Step 3:** Divide both sides by 4 y = 16 ÷ 4 = **4** Check: 7(4) - 4 = 28 - 4 = 24, and 3(4) + 12 = 12 + 12 = 24 ✓ --- **Why the wrong options tempt you** - **y = 2** comes from mistakenly doing 12 - 4 = 8, then 8 ÷ 4 = 2 (forgetting to properly collect terms) - **y = 3** appears if you divide 12 by 4 too early, ignoring the -4 - **y = 8** tricks you if you forget to divide by the coefficient: 12 + 4 = 16, but you must still divide by 4 --- **Quick takeaway** Collect like terms first (all y's together, all numbers together), *then* divide by the coefficient — never skip that final division!