Question if-x-i

2.2 Nonlinear Equations in One Variable - Quadratic solving (factoring, quadratic formula, completing square)
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the fraction with numerator 1, and denominator x squared, plus 10 x, plus 25, end fraction, equals 4

If x is a solution to the given equation, which of the following is a possible value of x plus 5 ?

A.

one half

B.

five halves

C.

nine halves

D.

eleven halves

If x is a solution to the given equation, which of the following is a possible

Hard-difficulty · SAT Math · Nonlinear Equations in One Variable — Quadratic solving (factoring, quadratic formula, completing square). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice A is correct. The given equation can be rewritten as the fraction 1 over, open parenthesis, x plus 5, close parenthesis, squared, end fraction, equals 4. Multiplying both sides of this equation by open parenthesis, x plus 5, close parenthesis, squared yields 1 equals, 4 times, open parenthesis, x plus 5, close parenthesis, squared. Dividing both sides of this equation by 4 yields one fourth equals, open parenthesis, x plus 5, close parenthesis, squared. Taking the square root of both sides of this equation yields one half equals, x plus 5 or negative one half equals, x plus 5. Therefore, a possible value of x plus 5 is one half.
Choices B, C, and D are incorrect and may result from computational or conceptual errors.