What is the solution to the given inequality?
1 answer:
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Answer:
C. is the correct option
C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3
and x = - 14
Step-by-step explanation:
8 ^ (x + 3) = 2 ^ (2x - 5)
Here is how the student solved the equation
8 ^ (x + 3) = 2 ^ (2x - 5)
8 ^ (x + 3) = 2 ^ (2x - 5)
(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)
2 ^ (3x + 3) = 2 ^ (2x - 5) ----- This is where the student made the error.
The student did not distribute 3 in * (2 ^ 3) ^ (x + 3).
This is how to solve the equation
8 ^ (x + 3) = 2 ^ (2x - 5)
8 ^ (x + 3) = 2 ^ (2x - 5)
(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)
Then, we will 3 distribute in (2 ^ 3) ^ (x + 3), so that we get
2 ^ (3x +9) = 2 ^ (2x -5)
Since the bases on both sides of the equation are equal, we can equate the powers so that we get
(3x +9) = (2x -5)
Then we will collect like terms
3x - 2x = -5 -9
∴ x = -14
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