sat-dog

- Choice B is correct. Multiplying each side of the given equation by 16 yields 2 + = 64 112x 576x. To complete the square, adding 49 to each side of this 2 + + = + ( )+2 = equation yields 64 112x 49 x576 49, or 8x 7 625. Taking the + = square root of each side of this equation yields two equations: 8x 7 25 and + =- + = 8x 7 25. Subtracting 7 from each side of the equation 8x 7 25 yields = =18 =9 8x 18. Dividing each side of this equation by 8 yields x , or x . 8 4 9 Therefore, is a solution to the given equation. Subtracting 7 from each side of 4 + =- =- the equation 8x 7 25 yields 8x 32. Dividing each side of this equation =- 9 - by 8 yields x 4. Therefore, the given equation has two solutions, and 4. 4 9 9 Since is positive, it follows that is the positive solution to the given equation. 4 4 2 Alternate approach: Adding 4x and 7x to each side of the given equation =2 + - yields 0 4 7x 36x. The right-hand side of this equation can be rewritten as 2 + - - 4 x16 9x 3x6. Factoring out the common factor of 4x from the first two - terms of this expression and the common factor of 9 from the second two ( + )- ( + ) ( + ) terms yields x4 x 4 9x 4. Factoring out the common factor of x 4 ( -)( +) from these two terms yields the expression 4 x9 x4. Since this expression - = + = is equal to 0, it follows that either x4 9 0 oxr 4 0. Adding 9 to each side - = = of the equation x4 9 0 yieldxs 4 9. Dividing each side of this equation by 4 =9 9 yields x . Therefore, is a positive solution to the given equation. Subtracting 4 4 + = =- 4 from each side of the equatioxn 4 0 yields x 4. Therefore, the given 9 - 9 9 equation has two solutions, and 4. Since is positive, it follows that is the 4 4 4 positive solution to the given equation. 7 Choice A is incorrect. Substituting for x in the given equation yields 4 -49=- 36, which is false. Choice C is incorrect. Substituting 4 for x in the given 2 - =- equation yields 92 36, which is false. Choice D is incorrect. Substituting 7 - =- for x in the given equation yields 245 36, which is false. 47 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnnnn MATH: MODULE 2