Solve: 4x - 3 = 2x + 7.

**The reasoning** This is a **linear equation** problem. Your goal: get all the x terms on one side and all the numbers on the other. Starting with: 4x - 3 = 2x + 7 **Step 1:** Subtract 2x from both sides (to collect x terms together) 4x - 2x - 3 = 2x - 2x + 7 2x - 3 = 7 **Step 2:** Add 3 to both sides (to isolate the x term) 2x - 3 + 3 = 7 + 3 2x = 10 **Step 3:** Divide both sides by 2 x = 5 **Check:** 4(5) - 3 = 20 - 3 = 17, and 2(5) + 7 = 10 + 7 = 17 ✓ **Why the wrong options tempt you** - **x = 2** comes from adding the coefficients wrongly (4 + 2 = 6, then 10 ÷ 6) - **x = 10** is what you get if you forget to divide by 2 at the end (stopping at 2x = 10) - **x = 4** appears if you subtract instead of add when moving -3 across (7 - 3 = 4, then forgetting the coefficient) **Quick takeaway** Always move x terms to one side and numbers to the other, then isolate x — and **verify your answer** by substituting back!