Solve for x: 3x - 7 = 2x + 5.

• A. 12
• B. 0
• C. -4
• D. 7

Answer: (A)

Solving linear equations means isolating the unknown by keeping both sides balanced as you move terms. For 3x - 7 = 2x + 5, start by removing 2x from the side with x to bring all x-terms to one side: 3x - 7 - 2x = 5, which simplifies to x - 7 = 5. Then undo the minus seven by adding seven to both sides: x = 12. A quick check shows this works: substitute 12 back in, left side is 3(12) - 7 = 29, right side is 2(12) + 5 = 29, matching. The other suggested values fail the equality when substituted; for instance, x = 0 gives -7 on the left and 5 on the right, x = -4 gives -19 and -3, and x = 7 gives 14 and 19. So the correct solution is x = 12.