Solve: 4x − 3 = 2x + 7.

## The reasoning This is a **linear equation** — we need to get all the x's 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 the 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 it:** 4(5) − 3 = 20 − 3 = 17, and 2(5) + 7 = 10 + 7 = 17 ✓ ## Why the wrong options tempt you - **x = 2**: You might get this if you subtracted 4x instead of 2x, or mixed up the signs - **x = 10**: This is what 2x equals, not x itself — forgetting that final division step - **x = 4**: Probably from arithmetic errors when adding/subtracting the constants ## Quick takeaway **Always move variables to one side, constants to the other, then solve — and CHECK your answer by plugging it back into the original equation!**