SAT Math Multiple Choice Practice Question 10: Answer and Explanation
10. If , then x equals
Correct Answer: C
C. On the real SAT, try all the numbers by plugging them in; doing so is usually faster than working out the problem. I do it the long way here, though, so you can practice your algebra skills. Start by cross-multiplying to get (x - 1)(x + 2) = (x + 7)(x - 2). Now you can use FOIL (a technique I explain in Chapter 14) to get x2 + 2x - 1x - 2 = x2 - 2x + 7x - 14. Simplifying each side, you get x2 + x - 2 = x2 + 5x - 14. A neat thing happens when you start to combine the like terms on different sides. You can subtract x2 from both sides, which means that both x2 terms just disappear, leaving you with the simple linear equation x - 2 = 5x - 14. Subtracting x from both sides yields -2 = 4x - 14. Now you add 14 to each side to get 12 = 4x, and x = 3.