SAT Math Multiple Choice Practice Question 72: Answer and Explanation

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Question: 72

6. Question below deals with the equation , where .

When the equation has a solution, x =

D. b + 2
E. a - 2b

Correct Answer: B


B. When solving an equation like this one, some people are more comfortable making both sides into fractions. So you can write and then cross-multiply to get ax = b(x + 2), or ax = bx + 2b. To solve for x, you need all the xs on one side, so subtract bx from both sides to get ax - bx = 2b. Now, because x is in both terms on the left side, you can factor it out: x(a - b) = 2b. And, finally, dividing by a - b gives you , which is Choice (B).

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