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Grade: 12

                        

The equation 47−x25+ 2 x24 2−xa = − 8 x − 3 − 53 2−xa is true for all values of x ≠ 2 a , where a is a constant. What is the value of a? A) -16 B) -3 C) 3 D) 16

2 years ago

Answers : (1)

dheeraj
20 Points
							

ANSWER EXPLANATION: There are two ways to solve this question. The faster way is to multiply each side of the given equation by 2−xa (so you can get rid of the fraction). When you multiply each side by 2−xa, you should have:

53−)2−xa()3−x8−(=47−x25+2x24

You should then multiply )3−x8−( and )2−xa( using FOIL.

53−6+x16+xa3−2xa8−=47−x25+2x24

Then, reduce on the right side of the equation

47−x16+xa3−2xa8−=47−x25+2x24

Since the coefficients of the 2x-term have to be equal on both sides of the equation, 24=a8−, or 3−=a.

The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and I do not recommend it for the actual SAT as it will waste too much time.

The final answer is B.

2 years ago
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