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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
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+2x24You should then multiply )3−x8−( and )2−xa( using FOIL.53−6+x16+xa3−2xa8−=47−x25+2x24Then, reduce on the right side of the equation47−x16+xa3−2xa8−=47−x25+2x24Since 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.
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.
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