Find the value of x such that 8x-3= 164-x
Correct answer: D. 25/7
- A. 4
- B. 11/3
- C. 7/2
- D. 25/7
Explanation
To solve 8x-3 = 164-x, express both numbers as powers of 2: 8 = 23 and 16 = 24. Thus, rewrite the equation as (23)x-3 = (24)4-x. This simplifies to 23(x-3) = 216-4x. Since the bases are the same, equate the exponents: 3(x-3) = 16-4x. Solving for x gives 3x - 9 = 16 - 4x, leading to 7x = 25, so x = 25/7.The other options (4, 11/3, and 7/2) do not satisfy this equation when substituted back, indicating errors in setting up or solving the equation.
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