Final answer:
We solved the equation by multiplying both sides by the reciprocal of 5/8 and then simplifying. The correct answer to g5/8 = 12/9 is approximately 2.1, which isn't listed in the provided answer choices. The closest option given is 4) g = 3.3, but it is still not accurate.
Step-by-step explanation:
We are asked to solve for g in the equation g5/8 = 12/9. To do this, we must isolate g on one side of the equation. We start by multiplying both sides of the equation by the reciprocal of 5/8, which is 8/5. This step cancels out the 5/8 on the left side and we get g = (12/9) × (8/5).
Next, we simplify the right side of the equation by multiplying the numerators together and the denominators together. Doing this, we get g = (12 × 8) / (9 × 5) which simplifies to g = 96/45. Dividing both the numerator and the denominator by their greatest common divisor, which is 3, we get g = 32/15. Finally, converting this to a decimal gives us g = 2.133....
Checking our answer choices, none of them exactly match the answer we have computed. Therefore, there may be a typo or mistake in the provided answer choices. If rounded to one decimal place, 2.133... would be approximately 2.1, which is not listed among the answer choices. Based on the calculation, option 4) g = 3.3 is the closest, but still not accurate